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:ii 



EASY LESSONS 



ON 



REASONING 



By 



I 



RICHARD WHATELY, U.D., 

ARCHBISHOP OF DUBLIN. 



THIRD AMERICAN 



FIFTH LONDON EDITION. 



;^oF so,-;7- 




/* o BOSTON: 
WILLIAM H. .DEISNET. 

1868, 



,a'^ 



% 



^"Wsl 



Entered according to Act of Congress, in the year 1868, 

By WILLIAM H. DENNET, 

In tho Clerk'-. Office of the District Court of the District of Mas^achasetts. 



Cambridge: Presswork by John Wilson and Son. 




PREFACE. 



The subject treated of iu the following pages is one whicli has 
not usually been introduced into the course of elementary studies 
for young persons of all classes. 

It is supposed by some that the difference between a better and 
a worse reasoner depends either wholly on natural ability, or on 
that combined with practice, or on each man's greater or less pro- 
ficiency iu the subjects he is treating of. 

And others again consider a systematic study of the principles 
of Reasoning as suitable only to a few persons, of rare endowments, 
and of a peculiar turn of mind ; and to those, only in an advanced 
stage of their education. 

That this branch of study is requisite for all, and is attainable 
by all, and presents not, necessarily, any greater difficulties than 
the rudiments of Arithmetic, Geometry, and Grammar, — all this 
cannot be so well evinced in any other way as by experiment. If 
the perusal of these Lessons, or of the half of them, fail to satisfy 
on this point any tolerably attentive reader, it is not likely he 
would be convinced by any distinct argument to the same effect 
that could be offered. 

The work has very little claim to novelty, except as to the 
simplicity and famiharity of its form. But without making any 
discovery, strictly so called, of any thing previously altogether un- 
known, it is possible — since ' discovery ' is a relative word — to be, 
practically a discoverer, by bringing within the reach of thousands 
some important branch of knowledge of which they would otherwise 
have remained destitute all their lives. 

And in regard to the present subject, a familiar introduction to 
the study is precisely what has hitherto been wanting. The exist- 
ing treatises upon it may be compared to ships, well freighted, but 
which can only unlade at a few wharves, carefully constructed, in 



4 PREF'ACE. 

advantageous situations. The want is, of small boats drawing very 
little water, wMch can carry ashore small parcels of the cargo on 
every part of the coast, and run up into every little creek. 

Should the attempt to supply this deficiency prove as successful 
as there is reason, from the trial that has been already made in the 
(^Saturday Magazine,} to hope, an addition by no means unimpor- 
tant will have been made to the ordinary course of elementary 
edu :ation. 

To frame, indeed, a system of rules that should equalize persons 
of all varieties of capacity, would be a project no less chimerical 
in this than in any other department of learning. But it would 
certainly be a great point gained, if all persons were taught to ex- 
ercise the reasoning faculty as well as the natural capacity of each 
would permit; for there is good reason to suspect that, in this 
point, men fail quite as often from want of attention, and of sys- 
tematic cultivation of their powers, as from natural deficiency. 
And it is at least worth trying the experiment whether all may 
not be, in some degree, trained in the right exercise of a faculty 
which all, in some degree, possess, and which all must, more or 
less, exercise, whether they exercise it well or ill. 

It was at one time contemplated to subjoin an Index of the 
technical terms, with brief definitions of them, and references to 
the Lessons and Sections. But, on second thoughts, it has been 
judged best to omit this, and to recommend each student to draw 
up such an index for himself. It is for students, strictly so called, 
— that is, persons employed in acquiring an elementary knowledo-e 
of the subject — that the work is chiefly designed : and for these, 
no exercise could be devised more calculated to facilitate their 
study than that of carefully compiling an Index, and also expand- 
ing the Table of Contents, so as to give a brief summary of the 
matter of each Lesson. And this being the case^ it would not be 
any real saving of labor to the learner to place before him such an 
Index and Table of Contents already drawn up. 

It may be worth while to suggest to the Teacher to put before 
his pupils, previously to their reading each Lesson, some questions 
pertaining to the matter of it; requiring of them answers, oral or 
written, the best they can think of without consulting, the book 
Next, let them read the Lesson, having other questions, such aa 



PREFACE. 5 

may lead to any needful explanations, put before them as they 
proceed. And afterwards let them be examined, (introducing 
numerous examples framed by themselves, and by the teacher,) as 
to the portion they have learned, in order to judge how far they 
remember it. 

Of these three kinds of questions, — which may be called, i. 
Preliminary questions ; ii. questions of histruction ; and iii. ques- 
tions of examination^ — the last alone are, by a considerable portion 
of Instructors, commonly employed. And the elementary books 
commonly known as ' catechisms,' or ' books in question and 
answer,' consist in reality of questions of this description. 

But the second kind, — what is properly to be called instructive 
questioning, — is employed by all who deserve to be reckoned 
good teachers. 

The third kind, — the preliminary questioning — is employed, 
(systematically and constantly) but by few. And at first sight it 
might be supposed by those who have not had experience of it, 
that it would be likely to increase the learner's difficulties. But if 
any well-qualified Instructor will but carefully and judiciously try 
the experiment, (in teaching any kind of science,) he will be sur- 
prised to find to how great a degree this exercise of the student's 
mind on the subject will contribute to his advancement. He will 
find that what has been taught in the mode above suggested will 
have been learnt in a shorter time, vdll have been far the more 
thoroughly understood, and will be fixed incomparably the better 
in the memory. 



1* 



INTRODUCTION 

TO THE AMEEICAN EDITION. 

The author of this little work has not, so far as we know, 
avowed himself. From internal evidence, one would infer very 
decidedly that the work was prepared by Dr. Whately. It is 
marked on every page by that same strong good sense and solid 
learning which have rendered his works on Logic and Rhetoric so 
eminently valuable as text-books for students. 

Many persons of high reputation for their attainments in those 
branches of learning to which they may have been devoted, have 
failed disgracefully, in the attempt to furnish a suitable text-book 
for the young student. Hence it is, that, although most depart- 
ments of science and literature have been cultivated with con- 
stantly increasing success, still the number of really good text-books 
is exceedingly small. 

The vanity of authorship has contributed much to this result. 
The writers of text-books for colleges and schools, have been too 
often tormented with the sorry ambition of saying something ori- 
ginal, or something fine. They have been prone to forget that 
orlginaKty, as such, is not to be sought for in a work for learners. 
They have been impatient of the careful thought, and literary 
self-denial, requisite to enable a man to say just what is necessary, 
and no more. Often, too. mistaking prolixity for clearness, they 
have burdened and perplexed the minds of the unlearned, with a 
multitude of vague terms, suggesting many ideas partially, but 
without giving distinct and sharply-defined views of any. 

The highest merits of a text-book are brevity, strict method in 
the arrangement, clearness and pertinency in the statement and 
illustration of what are the admitted principles of the subject 
treated upon. It is bare justice to say, that the elementary trea- 
tises of Dr. Whately are free from most of the defects, and comprise 



INTRODUCTION. 7 

most of the excellences above named. Whether he is the author 
of this work or not, it shows all the peculiar skill in arrangement, 
power of definite statement, and graphic illustration, which so 
strongly characterize his avowed works. To say the least, the 
freest use has been made of Whately's thoughts and language. 

The work contains the main principles of the Logic of Whately, 
somewhat divested of their technical form, but not of their scien- 
tific accuracy. There are also a few pages showing the application 
of Logic to the purpose of conviction, which would more strictly 
come under the head of Rhetoric. Although the author evidently 
intended the work for the younger classes of learners, it contains 
the distinct outlines of a system of Logic, and whoever thoroughly 
masters this little work, and becomes able to apply its principles 
to the analysis of arguments, will be no contemptible logician. 
It is thought that this book will be admirably adapted to the 
wants of the advanced classes in our High Schools and Academies, 
as well as to the wants of those who wish for some acquaintance 
with the theory of reasoning, and have not the time or the resolu- 
tion to go through any larger treatise on the subject. As a text- 
book for students in college, it is, doubtless, a more thorough work 
than that of Hedge, which holds its place in the list of text-books 
in some of our colleges. 

However well adapted this work may be to the young and 
uninstructed, as a digest of the science and art of reasoning, 
it may become still more valuable to them, as a discipline for 
the mind. It cannot have escaped the notice of attentive ob- 
servers, that the vast number of 'simplified' books, which have 
been prepared for the young, proposing to conduct them to learning 
by a royal road, have had an injurious influence. The practice of 
imparting knowledge in infinitesimal doses, diluted by leading 
questions and useless explanations, till it becomes tasteless, is very 
well, if the only object desired is to relieve the student from the 
labor of thinking. Though this object be attained, the process 
will have the efiect to weaken the power of attention, to destroy 
the robustness and vigor of the mind, and to pall that eager curi- 
osity which nature intended to sustain us under the protracted 
efibrt necessary to accomplish a difficult task. It cannot but have 
a salutary influence upon a young or undisciplined mind, to be 



8 INTRODUCTION. 

brought in contact with the clear and vigorous thinking of such a 
man as the author of this little work. The comparative abstruseness 
of the subject of the book, thus becomes one of its best recommenda- 
tions. Strong studies only can make strong men. Besides, the really 
efficient teacher will always find that the more difficult the subject, 
(provided it be fairly within the grasp of the pupil,) the greater will 
be the interest manifested. There is a pleasure in the act itself of 
overcoming difficulty, which excites the generous mind, and throws 
a lively interest around the investigation of the abstrusest subject. 

There may be those who object to Logic as entirely barren and 
useless. To such we would recommend a careful perusal of the 
larger work of Whately. The common objections to Logic, which 
have been echoed by hosts of writers, from Locke and the Scotch 
Metaphysicians, and have been rendered respectable by the au- 
thority of those great names, have been disposed of by Whately in 
such a way, that no scholar will again attempt to revive them. In 
the minds of those, however, who readily admit the value of 
Logic as a part of a course of college study, objections may 
arise to its introduction as a constituent element of popular 
education. 

Still it is believed that the objections that may be urged against 
the use of such a work as this, in schools and academies, will lie 
with equal propriety against almost all the scientific instruction 
ordinarily given in such institutions. The elements of Mathemat- 
ics, of Natural Philosophy, of Chemistry, and Natural History, 
have by general consent taken their place among the branches 
taught in schools, and for good reason. These sciences relate to 
the subjects with which, and upon which, we are constantly en- 
gaged in the active duties of life. Aside from prudential consider- 
ations, it is a gratification of the highest kind to the practical man, 
to be able, in a partial manner even, to refer the phenomena of 
nature around him to the general laws by which they are governed. 
Although the knowledge of such men must, of necessity, be super- 
ficial, compared with that of the man of science, still, it is gratify- 
ing to reflect that from this slight acquaintance with natural laws, 
the noblest practical inventions have often sprung. Not to limit 
that much abused term practical, to a narrow sense — how expansive 
and elevating are such truths to the mind of the learner, however 



INTRODUCTION. » 

imptrfectly conceived ! No teacher can have failed to perceive the 
effect often produced by tJie first introduction into the mind of the 
great principles of the laws of physics. The theory of reasoning 
has, however, a more extended bearing upon man, — his enjoy- 
ments and his capabilities, — than either, or all of these. If the 
science and art of reasoning be applicable at all, it is applicable to 
every thing. If it is of practical value to any, it is to all, and it 
has the most important and intimate connection with every art 
and science, and with the conduct of affairs in every possible situa- 
tion in life. The process of reasoning, as such, being the same in 
all cases, Logic has to do with every possible exercise of the rea- 
soning faculty. The more accurate the definitions, and the more 
obvious the data, of any science, the more easily can its deductions 
be subjected to Logical Analysis. Consequently, Mathematical 
reasonings, depending as they do upon postulates and definitions, 
(which, referring to quantity and space, are capable of distinct and 
unambiguous statement,) fall with the utmost readiness into logical 
formulas. The constant business, then, of a reasonable being, is to 
draw conclusions from things admitted. On the soundness of ar- 
guments, as well as upon the truth of facts, we are constantly ac- 
customed to stake the most vitally important interests. Not only 
do our most valued interests constantly depend on the soundness 
of our own conclusions, but often on the reasonings of others. We 
are, under God, dependent for our national existence and national 
blessings, on the soundness of the conclusions which are arrived at 
by the millions of voters in our land. No attempt, however inad- 
equate and feeble it may be, to infuse intellectual health into this 
great mass of reasoning power, can be unworthy of our regard. 
Is it a small matter that the rank and file of our voters should be 
able to analyze and determine the soundness or unsoundness of 
those arguments on Politics, or Public Economy, by which they 
are urged to support, or destroy, systems of public policy ? How 
often, within a few months, when listening to political haranguers, — 
discoursing with a logic worthy of the grave-diggers in Hamlet, — 
have we wished to be able to put into the possession of the lis- 
tening throng around, a power of analysis, which, like the spear of 
Ithuriel, might show in its genuine form the grossness of the impo- 
eition practised upon them. 



10 INTRODUCTION. 

It may be said that Logic will not remedy the evil, for h 
will not teach the ignorant political economy or history. True ; 
but it will enable them, at least, to detect unsound reasoning, 
when drawn from simple principles and familiar facts. Be- 
sides, the great majority of those who are dupes of others, or 
who deceive themselves by specious fallacies, suffer not so much 
from ignorance of facts and principles as from vague ideas of the 
relations which these facts and principles, bear to each other, and 
to the conclusions drawn from them. Unpractised in abstraction, 
such persons are unable to fix the mind steadily upon the point at 
issue in an argument, to the exclusion of what is irrelevant. It is 
a wise remark of Dr. Barrow, that ' confusion is the mother of 
iniquity.' To no case does this maxim apply with more force than 
to that confusion of thought, and indistinctness of mental vision, 
which disqualify a man for ascertaining the justness or fallacy of an 
argument, in reference to those subjects that vitally affect the 
peace and welfare of society. The constant resort of sophistical 
advocates, and politicians, and, indeed of errorists of every class, 
is the false issue, or in logical language, the irrelevant conclusion. 
Something is proved, triumphantly it may be, but not the thing 
requisite, and the conclusion thus obtained is adroitly shifted, un- 
der the cover of a cloud of words, and is affirmed with the utmost 
seriousness, of an entirely different subject. So long as the com- 
munity at large will be misled by fallacious reasoning, bad men 
will make use of it for their own advancement. 

Let students in our High Schools and Academies be as well 
taught in the analysis of arguments, as they are in the elements of 
other branches of learning, and it will not be unreasonable to hope 
that a salutary effect may be produced upon those who assume to 
instruct the people in Politics and Religion. Public men under- 
stand their own interests too well to deal in -counterfeits, when 
there is much danger of detection. There is much said of the de- 
plorably low standard of attainment to which professional men are 
contented to arrive. The surest way to secure honesty and intel- 
lectual ability, in the professions, is to create a demand for those 
qualities, by instructing those from whom the substantial rewai'ds 
of professional merit must come. Let the study of a book like this 
become general, and something, at least, Avill have been done 



INTRODUCTION. 11 

towards staying the floods of solemn nonsense, that, by the aid of 
the franking privilege, are yearly spread over our land. 

It is to be hoped that this little work will receive the attention 
from teachers and those interested in education, which its intrinsic 
excellence and the importance of the subject demand. 

JunCy 1845. 



EASY LESSONS ON REASONING. 



PART L 
ANALYTICAL INTRODUCTION. 



LESSON i 



N. B. In these Lessons, whenever two equivalent words or phrases are 
employed, one of them is enclosed in angular [brackets,] instead of the 
common mark of a (parenthesis;) 



§ 1. Every one is accustomed, more or less, to employ 
Reasoning. There is no one that does not occasionally at- 
tempt, well or ill, to give a Reason for any opinion he 
entertains ; — to draw Conclusions from what he sees around 
him, — to support those conclusions by some kind of Argu- 
ments, good or bad, — and to answer the arguments brought 
against him. 

Now all these expressions, — * giving a reason ' — ' draw- 
ing a conclusion ' — ' bringing forward an argument ' — re- 
late to one and the same process in the mind, that which is 
properly called 'Reasoning.' And the same may be said of 
several other expressions also; such as * inferring' or 
'drawing an inference,' — 'proving a point,' — 'establishing 
a conclusion,' — ' refuting an argument,' — &c. All these 
expressions, and some others besides, have reference, as we 
have said, to the process of Reasoning. 
2 



14 ANALYTICAL INTRODUCTION. \_Part I. 

§ 2. And this process, it is important to observe, is, in 
itself, universally, the same ; however different the subject- 
matter of our reasoning may be, on different occasions. 

The same is the case with Arithmetic. We may have to 
add, or subtract, multiply, or divide, certain numbers, either 
of Pounds-sterling, or of men, or of bushels of corn, &c. ; 
but though these are very different things, the arithmetical- 
process itself, in each of the operations, respectively, is always 
the same. For instance, to ' multiply ' always means to take 
one number a certain number of times ; whether it be men, 
or miles, or days, that we are numbering. 

So it is also with Grammar. The Nouns, and Verbs, and 
other Parts of Speech that Grammar treats of, may relate 
to very different subjects, and may be found in various kinds 
of Compositions ; such as works of Science, History, Poetry, 
&c., but the rules of Grammar are the same in all. 

So also the art of Writing (and the same may be said of 
Printing) is in itself the same, however different may be the 
kinds of subject-matter it is employed on. 

Now the same is the case (as has been above said) with 
Reasoning. We may be employed in reasoning on human 
affairs, or on Mathematics, or on Natural-history, or Chem- 
istry, or other subjects widely different from each other. 
But in every case the Reasoning-process is, in itself, the 
same. 

§ 3. Any Debate, [or Disputation] when you are endeav- 
oring to bring others over to your opinion, is one of the oc- 
casions on which Reasoning is employed; and the word 
* arguing ' is by some persons understood as having reference 
only to cases where there is a dispute between those who are 
maintaining opposite opinions. But this is a mistake. At 
least, it is a mistake to suppose that the use of ' Arguments ' 
— if we understand by that, the use of Reasoning — is con 
fined to the case of disputes; or even that this is the principal 



Lesson i.] the reasoning-process. 15 

employment of it. There is no set of men less engaged in 
dispute and controversy than Mathematicians ; who are the 
most constantly occupied in Reasoning. They establish all 
their propositions by the most exact proofs ; so complete as 
not even to admit of any dispute. 

And in all other subjects, likewise, a sensible man, when 
he wishes to make up his mind on any question, will always 
seek for some sufficient ' Reason ' [or ' Argument '] on which 
to found his conclusion. 

Thus, a Judge, before whom any Cause is tried, is occupied 
in weighing the Arguments on both sides, that are brought 
forward by the respective Advocates. He (no less than 
they) is engaged in Reasoning; though the Avoeates are 
disputing, and the Judge is not. 

A Physician, again, reasons from what he has read, and 
heard, and seen, in order to draw his conclusions on medical 
questions; — a Statesman, in political questions; — a Mer- 
chant, in mercantile matters ; and so, of the rest. 

§ 4. But when any dispute does take place, between per- 
sons of opposed opinions, it may be observed that the worst 
educated, — those who are the most unskilful in reasoning, or 
in clearly expressing their reasons, — are almost always the 
most apt to grow angry, and to revile each other, and quarrel. 

And even when they do not give way to anger, they 
usually, after a long discussion, part, without distinctly under- 
standing what the difference between them really consists in ; 
neither of them having clearly expressed his own meaning, 
or fully understood the other's. 

Indeed, it often happens that two persons who are dis- 
puting, do, in reality, disagree much less in their opinions 
than they themselves imagine ; or, perhaps, not at all. And 
hence it is that the word 'misunderstanding' has come to 
signify, a quarrel ; because quarrels so often arise from men's 
not clearly understanding each other's meaning. 



16 ANALYTICAL INTRODUCTION. [^jPart I. 

Again, it often happens that a person, not without good 
sense, will give such weak and absurd reasons for his opinion, 
— even when it is a right one, — that, instead of convincing 
others, he will even produce an opposite effect. 

§ 5. In order to avoid such inconveniences, and to conduct 
the process of Reasoning as clearly, as correctly, and as 
easily, as is possible, it is a great advantage to lay down ac- 
curate explanations of the principles on which Reasoning 
proceeds, and to employ, for the purpose, a technical lan- 
guage ; that is, a regularly-foi*med set of expressions, dis- 
tiQctly defined, and agreed on ; and to establish certain plain, 
simple rules, founded on, and expressed in. this technical 
language. 

Even in the common mechanical arts, something of a 
technical language is found needful for those who are learn- 
ing or exercising them. It would be a very great inconve- 
nience, even to a common carpenter, not to have a precise, 
well-understood name for each of the several operations he 
performs, such as chiseling, sawing, planing, &c., and for the 
several tools [or instruments] he works with. And if we 
had not such words as Addition, Subtraction, Multiplication, 
Division, &c., employed in an exactly defined sense, and also 
fixed rules for conducting these and other arithmetical pro- 
cesses, it would be a tedious and uncertain work, to go 
through even such simple calculations as a child very soon 
learns to perform with perfect ease. And after all, there 
would be a fresh difficulty in making other persons under- 
stand clearly the correctness of the calculations made. 

You are to observe, however, that technical language and 
rules, if you would make them really useful, must be not 
only distinctly understood, but also learnt, and remembered, as 
familiarly as the Alphabet ; and employed constantly, and 
with scrupulous exactness. Otherwise technical language will 
prove an incumbrance instead of an advantage ; just as a 



Lesson I.] THE REASONING-PROCESS. 17 

suit of clothes would be, if, instead of putting them on, and 
wearing them, you were to carry them about in your hand. 

§ G. It has been, accordingly, found advantageous, in what 
relates to the Reasoning-process, (as well as in the case of 
mechanical operations, and of calculations,) to lay down ex- 
planations, and rules, and technical terms; answering to those 
of Arithmetic, Grammar, and other branches of study. 

And the technical terms and rules, of Grammar, are not at 
all shorter, or easier to be understood and remembered than 
those pertaining to the present subject. 

You may, perhaps, meet with treatises professing much 
more than what we here propose ; — with works pretending 
to teach ' the right use of Reason ; ' (not Reason^7^^, or 
* Argumentation ' merely, but the whole of the Human In- 
tellect) and giving rules for forming a judgment on every 
question that can arise, and for arriving at all truths in 
any subject whatever. But such pretensions, however high- 
sounding and attractive, are fanciful and empty. One might 
as well profess to teach the * right use of the bodily-organs, 
and to lay down a system of rules that should instruct a mar 
in all manual arts and bodily exercises at once. 

If you do but teach a person to ride, or to draw, or to spin 
&c., something is gained : but if you should profess to la^; 
down a system of rules to teach all these at once, and also the 
business of a shipwright, and a musician, and a watchmaker, 
and everything else that is done by means of the bodily- 
organs, you would teach, in reality, nothing all. 

And so it is in all subjects. It is better to undertake 
even a little, that it is possible to accomplish, than to make 
splendid professions, which can only lead to disappointment. 

After all, indeed, it cannot be expected that, in Reasoning, 
any more than in other mental exercises, men of very un- 
equal degrees of intelligence should be brought to the same 
level. Nor is it to be expected that men will always be 

2* 



18 ANALYTICAL INTRODUCTION. ^Part I. 

* 

brought to an agreement in their conclusions. Different men 
will have received different information respecting facts ; or 
will be variously biassed, more or less, by their early preju- 
dices, their interests, or their feelings. 

But still, there is something gained, if they are taught, in 
respect of the Reasoning-process itself, how to proceed right- 
ly, and to express themselves clearly ; and if, when they do 
not agiee, they can be brought at least to understand wherein 
they differ, and to state distinctly what is ' the point at issue,' 
(as it is called) between them ; that is, what is the real ques- 
tion to be decided. 

And it is just so, in the case of Arithmetic also. Two 
persons may differ in their statements of an Account, from 
their settina: out with some difference in the numbers each 
puts down ; — in the Items (as it is called) of the Account. 
And no rules of Arithmetic can prevent such a difference as 
this. But it is something gained if they are guarded (as 
arithmetical rules do guard us) against differences arising 
out of errors in the calculation itself. 



LESSON n. 



§ 1. We have said that in all subjects, and on all occasions, 
the Reasoning-process is, in itself, the same. Whether you 
are occupied in refuting an opponent, or in conveying instruc- 
tion, or in satisfying your own mind on any point, — and 
again, whatever kind of subject-matter it is that you are en- 
gaged on, — in all cases, as far as you are (in the strict sense 
of the word) reasoning, — that is, employing Argument — it 
is one and the same process (as far as it is correctly con- 
ducted) that is going on in your own mind. 



Lesson ii.] the reasoning-process. 19 

And what this process is, must be the next point to be 
inquired into. 

Although (as has been said) all men do occasionally reason, 
they are often, at the time, as unconscious of it, as of the 
circulation of their blood, and the various other processes 
that may be going on within the body. And even when they 
do, knowingly and designedly, use arguments, or are listening 
to those of another, they will often be as much at a loss 
to explain why one argument appears to them strong, and 
another less strong, and another, utterly worthless, as if the 
whole were merely a matter of taste ; like their preference of 
one prospect, or one piece of music, to another. 

In order, then, to obtain correct rules for forming a judg- 
ment on this subject, and clear expressions for explaining 
such judgment to others, it is necessary to analyze, — as it is 
called, — (that is, take to pieces) the Reasoning-process. 
And for that purpose, we should begin . by examining the 
most plain, short, and simple arguments, and inquiring on 
what it is that their validity [or conclusiveness] depends, 
examining also some of those apparent-arguments which are 
not valid, and therefore are not, in reality, arguments at aU, 
though they are often passed off for them, as counterfeit coin 
is, for genuine. 

§ 2. You will perceive, on examination, that what is called 
a ' Conclusion,' — that is, a Proposition proved by Argument, 
— is drawn, in reality, from two other Propositions. And 
these are called its ' Premises ; ' from their being (in natural 
order) '• 'premised^ or put before it. 

At first sight, indeed, some might suppose that a Conclusion 
may follow from one Premise alone. For it happens oftener 
than not, that only one is expressed. But in this case there 
is always another Premise understood, and which is sup- 
pressed from its being supposed to be fully admitted. 

That this is the case, may easily be made evident, by sup- 



20 ANALYTICAL INTRODUCTION. [Part 1. 

posing that suppressed Premise to be denied ; which will at 
once destroy the force of the argument. For instance, if any 
one, from perceiving that ' the World exhibits marks of de- 
sign,' infers [or concludes] that ' it had an intelligent Maker,' 
he will easily perceive, on reflection, that he must have had 
in his mind another Premise also ; namely, that ' whatever 
exhibits marks of design, had an intelligent Maker : ' since if 
this last proposition were denied, the other would prove 
nothing. It is true, that, in some cases, one proposition im- 
plies another, by the very signification of the words, to every 
one who understands those words ; as, ' negroes are men ; 
therefore they are rational-beings : ' now ' rational-being ' is 
implied in the very name ' man.' And such examples as 
this, have led some people into the idea that we reason, — or 
that we may reason, — from a single premise. But take such 
a case as this ; some fossil-animal is discovered, which Natu- 
ralists conclude to have been a ' ruminant,' from its ' having 
horns on the skull.' Now, the laborers who dug up the 
skeleton could not draw this inference, supposing they were 
ignorant of the general law, ' that all horned animals are ru- 
minat : ' — and they might be thus ignorant, though using the 
name ' horned-animal ' in the same sense as the Naturalist : 
for the name itself does not imply ' ruminant,' as a part of 
its signification : and again, a Naturalist, at a distance, who 
knew the general law, but who had heard only an imperfect 
account of the skeleton, and did not know whether it was 
horned or not, would be equally unable to draw the inference. 

In all cases of what is properly called *• Argument,' there 
must be two premises assumed, whether they are both ex- 
pressed or not. 

§ 3. Such an argument as the above, when all the three 
propositions are stated at full length, and in their natural 
order, is called a ' Syllogism.' And this is the form in whicli 
all correct reasoning, an whatever subject, may be exhibited. 



Lesson ii.] the reasoning-process. 21 

When one of the Premises is suppressed, — [or, under^ 
stood'] which, for brevity's sake is usually the case, — the 
argument is called, in technical language, an ' Enthymeme : * 
a name derived from the Greek, and denoting that there is 
something left out, which is to be supposed [or understood] 
as being well-known. 

It is to be observed, that, when an argument, stated in 
this last form, is met by opponents, their objection will some- 
times lie against the assertion itself, that is made ; sometimes, 
against its force as an argument. They will say either ' I 
deny what you assume,^ or ' I admit, indeed, what you say, 
but I deny that it proves your conclusion.' For instance, in 
the example above, an atheist may be conceived either deny- 
ing * that that the World does exhibit marks of design, or 
again, denying f that \t follows from thence that it must have 
had an intelligent Maker. 

Now, you are to observe, that these are not, in reality, ob- 
jections of different kinds. The only difference is, that, in 
the one case, the expressed Premise is denied ; in the other, 
the suppressed Premise. For the force as an argument, of 
either Premise, depends on the other Premise. If either be 
denied, the other proves nothing. If both be admitted, the 
Conclusion regularly drawn from them, must be admitted. 

§ 4. It makes no difference in respect of the sense of an 
[argument, whether the Conclusion be placed last or first; 
i provided you do but clearly mark out what is the Conclusion. 

When it is placed last, (which is accounted the natural or- 
der) it is designated by one of those conjunctions called 
* illative,^ such as ' therefore,' — ' thence,' — ' consequently.' 

When the Conclusion is put first, the Premise is usually 
called the ' Reason ; ' and this is designated (whether it comes 



* As many of the ancient atheists did. 
t As most of the modern atheists do. 



22 ANALYTICAL INTRODUCTION. [^Part I. 

last or first) by one of the conjunctions called causal)' such 
as * since,' — ' because,' &c. 

And here it is to be observed that each of these sets of 
conjunctions have also another sense ; being used to denote, 
respectively, sometimes ' Premise and Conclusion,' — some- 
times ' Cause and Effect.' And much error and perplexity 
have often been occasioned by not attending to this dis- 
tinction. 

When I say ' this ground is rich ; because the trees on it 
are flourishing ; ' or again, when I express the same sense in 
a different form, saying, [ the trees on this ground are flourish- 
ing ; and therefore it must be rich,' it is plain that I am em- 
ploying these conjunctions to denote merely the connection of 
Premise and Conclusion ; or, (in other words) I am implying 
that the one may be inferred from the other. For it is evi- 
dent that the flourishing of the trees is not the cause of the 
ground's fertility, but only the cause of my believing it. The 
richness of the soU follows as an inference, from the luxuri- 
ance of the trees ; which luxuriance follows as an effect [or, 
natural consequence] from the richness of the soil. 

But if, again, I say, * the trees flourish, because the ground 
is rich,' or (which is the same in sense) * the ground is rich 
and consequently [or therefore] the trees flourish,' I am 
using the very same conjunctions in a different sense ; name- 
ly, to denote the connection of Cause and Effect. For in this 
case, the luxuriance of the trees, being a thing evident to the 
eye, would not need to be proved ; and every one would un- 
derstand that I was only accounting for it. 

§ 5. But again, there are many cases also in which the 
Cause is employed as an Argument, to prove the existence of 
its Effect. So that the Conclusion which, follows, as an In- 
ference, from the Premise, is also an Effect which follows 
naturally from that same Premise as its Cause. 

This is the kind of argument which is chiefly employed 



Lesson iii. fallacies. 23 

when we are reasoning about the future: as, for instance, 
when, from favorable or unfavorable weather, any one infers 
that the crops are likely to be abundant, or to be scanty. 

In such cases, the Cause, and the Reason [or Proof J coin- 
cide ; the favorable weather being at once the Cause of the 
good harvest, and the Cause of our expecting it. 

And this circumstance contributes to men's often con- 
founding together ' Cause ' and — what is strictly called — 
' Reason ; ' and to their overlooking the different senses of 
such words as * therefore,' * thence,' ' consequently,' &., and 
again, of such words as ' because,' ' inasmuch as,' &c., and 
also, of the words ' follow,' * consequence,' and several others ; 
which have all of them that double meaning which has been 
just explained. 



LESSON ni. 



§ 1. In such an argument as that in the example above 
given, (in § 2, Lesson ii.,) it is clearly impossible for any one 
who admits both Premises, to avoid admitting the Conclusion. 
If you admit that, ' Whatever exhibits marks of design, had 
an intelligent Maker,' and also, that ' the world exhibits 
marks of design,' you cannot escape the Conclusion, that 
* the world had an intelhgent Maker.' 

Or again, if I say, ' All animals with horns on the head 
are ruminant ; the Elk has horns on the head ; therefore it is 
ruminant ; ' it is impossible to conceive any one's doubting the 
truth of the Conclusion, supposing he does but allow the truth 
of each Premise. 

A man may, perhaps, deny, or doubt, and require proof, 
that all animals thus horned do ruminate. Nay, it is con- 



24 AlfALYTICAL INTRODlJCTION. {^Part I. 

ceivable that lie may even not clearly understand what 
'^ ruminant'' means; or he may have never heard of an 
'•Elk;'' but still it will be not the less clear to him, that, 
supposing these Premises granted^ the Conclusion must be 
admitted. 

And even if you suppose a case where one or both of the 
Premises shall be manifestly false and absurd, this will not 
alter the conclusiveness of the Reasoning ; though \\iq conclu- 
sion itself may, perhaps, be absurd also. For instance, ' All 
the Ape-tribe are originally descended from E-eptiles or In- 
sects : Mankind are of the Ape- tribe ; therefore Mankind are 
originally descended from Reptiles or Insects : ' here, every 
one * would perceive the falsity of all three of these proposi- 
tions. But it is not the less true that the conclusion yb/Zoi67s 
from those premises, and that if they were true, it would be 
true also. 

§ 2. But it often happens that there will be a seeming con- 
nexion of certain premises with a conclusion which does not 
really follow from them ; although, to the inattentive, or un- 
skilful, the argument will appear to be valid. And this is 
most especially likely to occur when such a seeming-argu- 
ment [or Fallacy] is dressed up in a great quantity of fine- 
sounding words, and is accompanied with much vehemence 
of assertion, and perhaps with expressions of contempt for 
any one who presumes to entertain a doubt on the matter. 
In a long declamatory speech, especially, it will often happen 
that almost any proposition at all will be passed off, as a 
proof of any other that does but contain some of the same 
tvords, by means of strenuous assurances that the proof is 
complete. 

Sometimes, again, sound arguments will be distrusted as 
fallacious ; especially if they are not clearly expressed ; and 
the more, if the conclusions are such as naen are not willing 
to admit. 

* Except certain French Naturalists. 



Lesson i.] arbitrary symbols. 2^) 

And frequently, also, when there really is no sound argument, 
the reader or hearer, though he believes, or suspects, that there 
is some fallacy, does not know how to detect and explain it. 

§ 3. Suppose, for instance, such seeming-arguments as the 
following to be proposed: — (1.) 'Every criminal is de- 
serving of punishment ; this man is not a criminal ; therefore 
he is not deserving of punishment : ' or, again, (2.) 'A]I 
wise rulers endeavor to civilize the People ; Alfred endeav- 
ored to civilize the People ; therefore he was a wise ruler.' 
There are, perhaps, some few persons who would not perceive 
any fallacy in such arguments, even when thus briefly and 
distinctly stated. And there are, probably, many who would 
fail to perceive such a fallacy, if the arguments were en- 
veloped in a cloud of words, and conveyed at great length in 
a style of vague, indistinct declamation ; especially if the 
conclusions were such as they were disposed to admit. And 
others, again, might perceive, indeed, that there is a fallacy, 
but might be at a loss to explain and expose it. 

Now, the above examples exactly correspond, respectively, 
with the following; in which the absurdity is manifest: — ■ 
(1.) ' Every tree is a vegetable ; grass is not a tree ; there- 
fore it is not a vegetable ; ' and (2.) ' All vegetables grow ; 
an animal grows ; therefore it is a vegetable.' These last 
examples, I say, correspond exactly (considered in respect 
of the reasoning) with the former ones ; the conclusions of 
which, however true, no more follow from the premises than 
those of the last. 

This way of exposing a fallacy, by bringing forward a 
similar one, where a manifestly absurd conclusion professes 
to be drawn from premises that are true, is one which we 
may often find it needful to employ when addressing persons 
who have no knowledge of technical rules ; and to whom, 
consequently, we could not speak so as to be understood, con- 
cerning the principles of Reasoning. 

3 



i^Q) ANALYTICAL mTRODUCTION. [^Part J. 

But it is evidently the most convenient, tlie shortest, and 
the safest course, to ascertain those principles, and on them 
to found rules which may be employed as a test in every case 
that comes 'before us. 

And for this purpose it is necessary (as has been above 
said) to analyse the Reasoning-process, as exhibited in some 
valid argument, expressed in its plainest and simplest form. 

§ 4. Let us then examine and analyse such an example as 
one of those first given : for instance, ' Every animal that has 
horns on the head is ruminant; the Elk has horns on the 
head ; therefore the Elk is ruminant.' It will easily be seen 
that the validity [or ' conclusivenes,' or ' soundness '] of the 
Argument does not at all depend on our conviction of the 
truth of either of the Premises ; or even on our understand- 
ing the meaning of them. For if we substitute some unmean- 
ing Symbol, (such as a letter of the alphabet,) which may 
stand for anything that may be agreed on — for one of the 
things we are speaking about, the Reasoning remains the 
same. 

For instance, suppose we say, (instead of ' animal that has 
horns on the head,') ' Every X is ruminant ; the Elk is X ; 
therefore the Elk is ruminant;' the argument is equally 
valid. 

And again, instead of the word ' ruminant,' let us put the 
letter ' Y : ' then the argument * Every X is Y ; the Elk is 
X ; therefore th^ Elk is Y ; ' would be a valid argument as 
before. 

And the same would be the case if you were to put ' Z ' for 
' the Elk : ' for the syllogism ' Every X is Y ; Z is X ; there- 
fore Z is Y,' is completely valid,, whatever you suppose the 
Symbols X, Y, and Z to stand for. 

Any one may try the experiment, by substituting for X, 
Y, and Z, respectively, any words he pleases ; and he will 
find that if he does but preserve the same/on?i of expression, 



Lesson iii.] arbitrary symbols. 27 

it will be impossible to admit the truth of the Premises, with- 
out admitting also the truth of the Conclusion. 

§ 5. And it is worth observing here, that nothing is so 
likely to lead to that — very common, though seemingly 
strange — error, of supposing ourselves to understand dis- 
tinctly what in reality we understand but very imperfectly, 
or not at all, as the want of attention to what has been just 
explained. 

A man reads — or even writes — many pages perhaps, of 
of an argumentative work, in which one or more of the terms 
employed convey nothing distinct to his mind : and yet he is 
liable to overlook this circumstance, from finding that he 
clearly understands the Arguments. 

He may be said, in one sense, to understand what he is 
reading ; because he can perfectly follow the train of Reason- 
ing, itself. But this, perhaps, he might equally well do, if he 
were to substitute for one of the words employed, X, or Z, or 
any other such unknown Symbol ; as in the examples above. 

But a man will often confound together, the understanding 
of the Arguments, in themselves, and the understanding of 
the words employed, and of the nature of the things those 
words denote. 

It appears, then, that valid Reasoning, when regularly ex- 
pressed, has its validity [or conclusiveness] made evident 
from the mere form of the expresssion itself, independently 
of any regard to the sense of the words. 

§ 6. In examining this form, in such an example as that 
just given, you will observe that in the first Premise (' X is 
Y, ') it is assumed universally of the Class of things (what- 
ever it may be) which ' X' denotes, that ' Y' may be affirmed 
of them : and in the other Premise, (' Z is X ') that ' Z ' (what- 
ever it may stand for) is referred to that Class, afs compre- 
hended in it. Now it is evident that whatever is said of the 
whole of a Class may be said of anything that is compre- 



28 ANALYTICAL INTRODUCTION. \_Part I. 

hended [or ' included,' or * contained/] in that Class ; so that 
we are thus authorized to say (in the conclusion) that ' Z ' is 

Thus also in the example first given, having assumed uni- 
versally, of the Class of ' Things which exhibit marks of 
design,' that they ' had an intelligent maker,' and then, in the 
other Premise, having referred ' The world ' to that Class, 
we conclude that it may be asserted of ' The world ' that ' it 
had an intelligent maker.' 

And the process is the same when anything is denied of a 
whole class. We are equally authorized to deny the same, 
of whatever is comprehended under that Class. For instance 
if I say, ' No liar is deserving of trust : this man is a liar ; 
therefore he is not deserving of trust : ' I here deny * deserv- 
ing of trust,' of the whole Class denoted by the word ' liar ; ' 
and then I refer ' this man ' to that Class ; whence it follows 
that ' deserving of trust ' may be denied of him. 

§ 7. This argument also will be as manifestly valid, if (as in 
the former case) you substitute for the words which have a 
known meaning, any undetermined Symbols, such as letters 
of the alphabet. * No X is Y ; Z is X ; therefore Z is not 
Y,' is as perfect a syllogism as the other, with the afirmative 
conclusion. 

To such a form all valid arguments whatever may be re- 
duced : and accordingly the principle according to which they 
are constructed, is to be regarded as the Universal Prin- 
ciple OF Reasoning. 

It may be stated, as a general Maxim, thus : ' Whatever is 
said, whether afiirmatively, or negatively,' [or ' whatever is 
afiirmed or denied '] * of a whole Class, may be said in like 
manner,' [that is ' affirmed in the one case, and denied in the 
other,'] ' of everything comprehended under that Class.' 

Simple as this Principle is, the whole process of Reasoning 
is embraced in it. Whenever we establish any Conclusion, 



Lesson iii.] principle op reasoning. 29 

— that is, show that one thing may allowably be affirmed, or 
be denied, of another — this is always in reality done by re* 
ferring that other to some Class of which such affirmation or 
denial can be made. 

The longest series of arguments, when fully unfolded, step 
by step, will be found to consist of nothing but a repetition of 
the same simple operation here described. But this circum- 
stance is apt to be overlooked, on account of the brevity with 
which we usually express ourselves. A Syllogism, such as 
those in the examples above, is seldom given at full length ; 
but is usually abridged into an ' Enthymeme.' * (See Less. 
II. § 3.) And moreover what is called ' an argument,' is 
very often not one argument, but several compressed together ; 
sometimes into a single sentence. As when one says, ' The 
adaptation of the instinct of suction in young animals to the 
supply of milk in the parent, and to the properties of the 
Atmosphere, as well as other like marks of design, show that 
^the world must have had an intelUgent Maker.' For most 
men are excessively impatient of the tedious formality of 
stating at full length anything that they are already aware of, 
and could easily understand by a slight hint. 



LESSON IV. 



§ 1. We have seen that when an Argument is stated in the 
regular form, (as in the foregoing examples,) which is what 
is properly c^led a ' Syllogism,' the validity [or conclusive- 
ness] of the reasoning is manifest from the mere form of the 
expression itself, without regard to the sense of the words ; 
so that if letters, or other such arbitrary unmeaning Symbols, 

* That is an argument with one of the Premises understood. 
3* 



30 ANALYTICAL INTRODUCTION. [Part I. 

be substituted, the force of the argument will be not the less 
evident. Whenever this is not the case, the supposed argu- 
ment is either sophistical and unreal, or else, may be reduced 
(without any alteration of its meaning) into the above form ; 
in which fonn, the general Maxim that has been laid down 
will apply to it 

What is called an unsound [or fallacious] argument (that 
is, an apparent-dLVgameni which is in reality none) cannot, of 
course, be reduced into such a form. But when it is stated 
in the form most nearly approaching to this that is possible, 
and especially when unmeaning Symbols (such as letters) are 
substituted for words that have a meaning, its fallaciousness 
becomes evident from its want of conformity to the above 
Maxim. 

§ 2. Let us take the example formerly given : Every crim- 
inal is deserving of punishment ; this man is not a criminal ; 
therefore he is not deserving of punishment : this, if stated in 
letters, would be * every X is Y ; Z is not X ; therefore Z is 
not Y.' Here, the term (' Y ') ' deserving of punishment ' is 
affirmed universally of the Class (X) 'criminal;' and it 
might therefore, according to the Maxim, be affirmed of any- 
thing comprehended under that Class ; but in the instance 
before us, nothing is mentioned as comprehended under that 
Class: only 'this man' ('Z') is excluded from that Class. 
And although what is affirmed of a whole Class may be 
affirmed of anything which that Class does contain, we are 
not authorized to deny it of whatever is not so contained. 
For it is evident that what is truly affirmed of a Class, may 
be applicable not only to that Class, but also to other things 
besides. 

For instance, to say that ' every tree is a vegetable ' does 
not imply that ' nothing else is a vegetable.' And so also, to 
say that ' every criminal is deserving of punishment,' does not 
imply that ' no others are deserving of punishment : ' for how 



Lesson iv. apparent-arguments. 31 

ever true this is, it has not been asserted in the proposition be- 
fore us. And in analysing an argument we are to dismiss all 
consideration of what might have been asserted with truth, 
and to look only to what actually is laid down in the 
Premises. 

It is evident therefore that such an apparent-argument as 
the above does not comply with the Rule [or Maxim] laid 
down ; nor can it be so stated as to comply with it ; and it is 
consequently invalid. 

§ 3. Again, let us take another of the examples formerly 
given ; ' All wise rulers endeavor to civilize the People ; 
Alfred endeavored to civilize the People ; therefore he v/as a 
wise ruler.* The parallel example to this, was, ' All vege- 
tables grow ; an animal grows : therefore it is a vegetable.' 
And each of these, if stated in Symbols, would stand thus : 
every ' Y is X,' [or the thing denoted by Y is comprehended 
under the Class for which X stands] ' Z is X ; therefore Z is 
Y.' 

Now in such an example, the quality of ' growing ' [X] is, 
in one Premise, afiirmed universally of Vegetable,' ['Y,'] 
and it might therefore have been affirmed of anything that 
can be referred to the Class of ' vegetable ' as comprehended 
therein : but then, there is nothing referred to that Class, in 
the other Premise ; only, the same thing which had been 
affirmed of the Class ' vegetable,' is again affirmed of another 
Class, 'animals' (Z) ; whence nothing can be inferred. 

Again, take such an instance as this ; * food is necessary to 
life ; com is food ; therefore corn is necessary to Kfe.' Here, 
* necessary to life ' is affirmed of ' food,' but not universally ; 
for every one would understand you to be speaking not of ' all 
food,' but of ' some food,' as being ' necessary to life.' So that, 
expressed in Symbols, the apparent-argument would stand 
thus : ' Some X is Y ; Z is X; therefore Z is Y ; ' in which 
you may see that the rule has not been complied with ; since 



32 ANALYTICAL INTRODUCTION. ^Part I, 

that which has been affirmed not of the whole of a certain 
Class, [or, not universally'] but only of part of it, cannot on 
that ground be affirmed of whatever is contained under that 
Class. 

§ 4. There is an argument against miracles by the well- 
known Mr. Hume, which has perplexed many persons, and 
which exactly corresponds to the above. It may be stated 
thus ; ' Testimony is a kind of evidence more likely to be false 
than a miracle to be true ; ' (or, as it may be expressed in other' 
words, we have more reason to expect that a witness should 
he, than that a miracle should occur) 'the evidence on which 
the Christian miracles are believed, is testimony ; therefore 
the evidence on which the Christian miracles are believed ia 
more likely to be false than a miracle to be true.' 

Here it is evident that what is spoken of in the first of 
these Premises, is, ' some testimony ; ' not ' all testimony,' [or 
any whatever,] and by ' a witness ' we understand, ' some wit- 
ness,' not, ' every witness ; ' so that this apparent-argument has 
exactly the same fault as the one above. And you are to 
observe that it makes no difference (as to the point now be- 
fore us) whether the word ' some ' be employed, or a diffisrent 
word, such as ' most ' or ' many,' if it be in any way said or 
implied that you are not speaking of ' alU For instance, 
^most birds can fly; and an ostrich is a bird,' proves nothing. 

§ 5. In order to understand the more clearly, and to des- 
cribe the more accurately, the fallaciousness of such seeming- 
arguments as those of which we have just given examples, 
and also, the conclusiveness of the sound arguments, it will be 
necessary to explain some technical words and phrases which 
are usually employed for that purpose. This is no less need- 
ful (as was remarked in Lesson I.) than for an Artisan to 
have certain fixed and suitable names for the several instni- 
ments he works with, and the operations he performs. 

The word ' Proposition,^ (which we have already had occa- 



Lesson iv.] technical tv^ords. 33 

sion to use) signifies ^ a Sentence in which something is sain 

— [or predicated] — that is, affirmed or denied — of another.' 
That which is spoken of, is called the * Subject ' of the propo- 
sition ; and that which is said of it is called the ' Predicate ; ' 
and these two are called the ' Terms ' of the Proposition ; from 
their being (in natural order) the extremes [or boundaries] 
of it. 

You are to observe that it matters not whether each of 
these Terms consist of one word, or of several. For whether 
a Proposition be short or long, there must always be in it, 
one — and but one — thing of which you are speaking ; which 
is called (as has been just said) the Subject of it : and there 
must be (in any one Proposition) one thing, — and only one 

— that is affirmed or denied of that Subject : and this which 
we thus affirm or deny of the other, is called -r— whether it be 
one word or more — the Predicate. 

§ 6. You are to observe also that though, (in our language) 
the Subject is usually placed first ; this order is not at all 
essential. For instance, ' it is wholesome to rise early,' or 
' to rise early is wholesome,' or ' rising early is wholesome,' 
are only three ways of expressing the same Proposition. In 
each of these expressions, ' rising early,' (or ' to rise early,' 
for these are only two forms of the Infinitive) is what you are 
speaking of ; and * wholesome ' is what you say [or predicaie~\ 
of it. 

When we state a proposition in arbitrary Symbols, as ' X 
is Y,' it is understood that the first term (' X ') stands for the 
Subject, and the last (' Y') for the Predicate. But when we 
use the terms that are significant, [or, have a meaning] we 
must judge by the sevise of the words which it is that is the 
Subject, and which the Predicate ; that is, we must ask our- 
selves the question * What am I speaking of? and what am I 
saying of it ? ' 

For instance, ' Great is Diana of the Ephesians ; ' here 



34 ANALYTICAL INTRODUCTION. [^Part I. 

' great ' is evidently the Predicate. Again, ' Thou art the 
man ; ' and ' Thou hast given occasion to the enemies of the 
Loid to blaspheme ; ' by asking yourself the above question, 
you will perceive, that in the former of these examples, ' Thou * 
is the Predicate, and in the latter, the Subject. 

§ 7. That which expresses the affirmation or denial, is call- 
ed the ' CopulaJ For instance, if I say, ' X is Y,' or ' X is 
not Y,' in each of these examples, 'X' is the Subject, and 
* Y ' the Predicate ; and the Copula is the word ' 2S ' in the 
one, and '■ is not,' in the other. 

And so it is, in sense, though not always in expression, in 
every Proposition. For either the Affirmative-copula, ' is ' or 
the Negative-copula, ^ is not,' must be always, in every Pro- 
position, either expressed in those words, or implied in some 
other expression. 

Any Sentence which does not do this — in short, which does 
not affirm or deny — is not a Proposition. For instance, of 
these sentences, ' are your brothers gone to school ? ' ^ they 
are not gone ; ' 'let them go,' the second alone is a Proposi- 
tion ; [or * Assertion 'J the first being a Quesiiony and the last 
a Commandf or request. 



LESSON V. 



§ 1. "We have seen that in every Proposition there is some- 
thing that is spoken of ; which is called the Subject; and 
something that you affirm or deny of it ; w-hich is called the 
Predicate. And it is evidently of great importance to under- 
stand and express clearly, in each Proposition, whether the 
Predicate is said of the whole of the Subject, or only of pa?-/ 



Lesson v.] propositions. 35 

of it : — in other words, whether it is predicated ' universally, 
or ^particularly.^ \J partially. '^ 

If, for instance, I say, or am understood to imply, that * all 
testimony is unworthy of credit,' this is a very different asser- 
tion from saying or implying, merely that ' some testimony is 
unworthy of credit.' The former of these is called a ' Uni- 
versal ' Proposition ; the Subject of it being taken universally 
as standing for anytfiing and everything that the Term is ca- 
pable of being applied to in the same sense. And a Term so 
taken is said (in technical language) to be ' distributed.' The 
latter of the two is called a ' Particular Proposition ; ' the 
Subject being taken particularly, as standing only for part of 
the things signified by it : and the Term is then said to be 
^ undistributed.' 

The technical word ' distributed ' (meaning what some wri- 
ters express by the phrase ' taken universally') is used, as you 
perceive in a sense far removed from what it bears in ordina- 
ry language. But, — for that very reason, — it is the less 
likely to lead to mistakes and confusion. And when once its 
technical sense is explained, it is easily remembered. When 
I say, ' birds come from eggs,' and again, ' birds sing,' I mean, 
in the former proposition, ' all birds ; ' [or ' every bird ' ] in 
the latter proposition, I mean, not,- ' all,' but ' some ' birds. In 
the former case the term ' birds ' - is said to be ' distributed ; ' 
in the latter ' undistributed.' You must be careful also to 
keep in mind the technical sense (already explained) of the 
word '■particular.' In ordinary discourse, we often speak of 
Hhis particular ^evson' or thing; meaning 'ihi^ individual.' 
But the technical sense is different. If I say ' this city is 
large,' the Proposition is not ' Particular,' but is equivalent to 
a Universal ; since I am speaking of the whole of the Sub- 
ject, which is, ' this single city.' But ' some city is large,' or, 
* some cities are large,' is a particular proposition ; because 
the Subject, ' city,' is taken not universally, but partially. 



36 ANALYTICAL INTRODUCTION. \^Pmi I. 

The distinction between a ' Universal ' proposition, and a 
* Particular,' is (as I have said) very important in Reasoning; 
because, as has been already remarked, although what is said 
of the whole of a Class may be said of anything contained in 
that Class, the Rule does not apply when something is said 
merely of j9«r^ of a Class. (See the example 'XisY'in 
§ 3 of the preceding Lesson.) 

§ 2. You will have seen that in some of the foregoing ex- 
amples, the words ' all,' ' every,' or ' any,' which are used to 
denote the distribution of a Subject, ^nd again, ' some,' which 
denotes its non-distribution, are not expressed. They are often 
understood, and left to be supplied in the reader's or hearer's 
mind. Thus, in the last example, 'birds smg,' evidently 
means ' some birds ; ' and, ' man is mortal,' would be under- 
stood to mean ' every man.' 

A Proposition thus expressed, is called ' Indefinite ; ' it be- 
ing left undetermined [' undefined '] by the form of expression, 
whether it is to be considered as Universal or as Particular. 
And mistakes as to this point will often give a plausible air to 
fallacies ; such as that in the last Lesson (§ 4.) respecting 
* Testimony.' 

But it is plain that every Proposition must in reality he 
either Universal or Particular ; [that is, must have its Sub- 
ject intended to be understood as distributed, or, as not dis- 
tributed] though we may not be told which of the two is 
meant. 

And this is called, in technical language, the distinction of 
Propositions according to their 'Quantity;' namely, into Ur.i- 
versal and Particular. ' Every X is Y ' and ' some X is Y,' 
are propositions differing from each other in their ' quantity,' 
and in nothing else. 

§ 3. But the Predicate of a proposition, you may observe, 
has no such sign as ' all ' or ' some,' affixed to it, which denote, 
when affixed to the Subject, the distribution, or non-distribu- 



Lesson v.] quality and quantity. 37 

tion of that term. And yet it is plain that each Term of a 
proposition, — whether Subject or Predicate — must always 
be meant to stand either for the whole, or for part, of what is 
signified by it ; — in other words, — must really he either dis- 
tributed or undistributed. But this depends, in the case of 
the Predicate, not on the * quantity ' of the proposition, but 
on what is called its ' Quality ; ' that is, its being Affirmative 
or Negative. And the invariable rule, (which will be ex- 
plained presently) is, that the Predicate of a Negative-propo- 
sition is distributed, and the Predicate of an Affirmative, un- 
distributed. 

When I say ' X is Y ' the term * Y ' is considered as stand- 
ing for part of the things to which it is applicable ; in other 
words, is undistributed. And it makes no difference as to 
this point whether I say ' all X,' or ' some X is Y.' The Pre- 
dicate is equally undistributed in both cases ; the only thing 
denoted by the signs * all ' or ' some/ being the distribution or 
non-distribution of the Subject. 

If, on the other hand, I say ' X is not Y,' whether meaning 
that ' No X is Y,' or that ' some X is not Y,' in either case, 
^ Y ' is distributed. 

§ 4. The reason of this rule you will understand, by con- 
sidering, that a Term which may with truth be affirmed of 
3ome other, may be such as would also apply equally well, 
and in the same sense, to something else besides that other. 
Thus, it is true that ' all iron is a metal,' although the term 
-metal' is equally applicable to gold, copper, &c., so that you 
could not say with truth that ' all metal is iron,' or that ' iron, 
and that only, is a metal.' For the term ' iron ' is of narrow- 
er extent than the term ' metal,' which is affirmed of it. 

So that, in the above proposition, what we have been com- 
paring, are, the whole of the term ' iron,' and part of the term 
* metal ; ' which latter term, consequently, is undistributed. 

And this application applies to ex^ery affirmative proposi- 
4 



38 ANALYTICAL LNTRUDUCTION. \^Part I 

tion. For though it may so happen that the Subject and the 
Predicate may be of equal extent [or ' equivalent ; ' or as 
some express it, ' convertible,'] so that the Predicate which is 
affirmed of that Subject could not have been affirmed of any- 
thing else, this is not implied in the expression of the proposi- 
tion itself. 

In the assertions, for instance, that ' every equilateral trian- 
gle is equiangular,' and that ' any two triangles which have all 
the sides of one equal to all the sides of the other, each to 
each, are of equal areas,' it is not implied that ' every equian- 
gular triangle is equilateral,' or that ' any two triangles of 
equal areas have their respective sides equal.' This latter in- 
deed is not true : the one preceding it is true ; that is, it is 
iTue that ' every equiangular triangle is equilateral,' as well 
ts that * every equilateral triangle is equiangular : ' but these 
Are two distinct propositions, and are separately proved in 
treatises of Geometry. 

If it happen to be my object to assert that the Predicate as 
well as the subject of a certain affirmative proposition is to 
be understood as distributed — and if I say, for instance, ' all 
equilateral triangles, and no others, are equiangular;,' — I am 
asserting, in reality, not one proposition, merely, but tivo. 
And this is the case whenever the proposition I state is under- 
stood (whether from the meaning of the words employed, or 
from the general drift of the discourse) to imply that the 
whole of the Predicate is meant to be affirmed of the Sub- 
ject. 

Thus, if I say of one number — suppose 100 — that it is 
the Square of another, as 10, then, this is understood by every 
one, from his knowledge of the nature of iiumhers, to imply, 
what are, in reality, the two propositions, that '100 is the 
Square of 10,' and also that 'the Square of 10 is 100.' 

Terras thus related to each other are called in technical 
language, '■ convei-tible' [or ' equivalent '] terms. But then. 



Lesson v.] convertible terms. 39 

jou are to observe that Avhen you not only affirm one term of 
another, but also affirm (or imply) that these are ' convertible ' 
terms, you are making not merely one assertion, but two, 

§ 5. It appears, then, that in affirming that ' X is Y,' I as- 
sert merely that ' Y ' — either the whole of it, or part, (it is not 
declared, which) is applicable to ' X ; ' [or ' comprehends,' or 
' contains ' X.] Consequently, if any part of a certain Pre- 
dicate be applicable to the Subject, it must be affirmed, — 
and of course cannot he denied — of that Subject. To deny 
therefore the Predicate of the subject, must imply that no part 
of the Predicate is applicable to that Subject ; in short that 
the whole Predicate is denied of that Subject. 

You may thus perceive that to assert that ' X is not Y ' is 
to say that no part of the term * Y ' is applicable to ' X : ' (for 
if any part were applicable, ' Y ' could be affirmed, and not 
denied, of ' X ') in other words, that the whole of ' Y ' is de- 
nied of 'X;' and that consequently 'Y' is 'distributed.' 
When I say, for instance, ' All the men found on that island 
are sailors of the ship that was wrecked there,' this might be 
equally true whether the whole crew or only some of them, 
were saved on the island. To say therefore that ' the men 
found on that island are not sailors of the ship, &c.' would be 
to deny that any part of that crew are there ; in short, it 
would be to say that the whole of that Predicate is iTiapplica- 
ble to that subject. 

§ 6. And this holds good equally whether the negative pro- 
position be ' universal ' or ' particular.' For to say that 'some 
X is not Y ' (or — which is the same in sense — that ' all X 
is not Y ') is to imply that there is no part of the term ' Y ' 
[no part of the class which ' Y ' stands for~\ that is applicable 
to the whole without exception, of the term ' X ; ' in short, that 
there is some part of the term ' X ' to which ' Y ' is wholly in- 
applicable. 

Thus, if I say, ' some of the men found on that island are 



40 ANALYTICAL INTRODUCTION. \_Part 1. 

not sailors of the. ship that was wrecked there/ or, in other 
words, * the men found on that island are not, all of them, 
sailors of the ship, &c.' I imply that the term ' sailors, &c.' is 
wholly inappUcable to some of the ' men on the island ; ' though 
it might perhaps be applicable to others of them. 

Again if I say ' some coin is made of silver,' and ' some 
coin is not made of silver ' (or in other words, that * all coin 
is not made of silver ') in the former of these propositions I 
imply, that in som£ portion (at least) of the Class of * things 
made of silver,' is found [or comprehended] ' some coin : ' 
m the latter proposition I imply that there is ' some coin ' 
which is contained in no portion of the Class of * things made of 
silver ; ' or (in other words) which is excluded from the whole 
of that Class. So that the term ' made of silver ' is distribut- 
ed in this latter proposition, and not, in the former. 

Hence may be understood the rule above given, that in all 
Affirmative-propositions the Predicate is undistributed, and in 
all Negative-propositions, is distributed. 

The ' Subject ' is, as we have seen above, distributed, in a 
Universal-proposition, (whether affirmative or negative,) and 
not in a Particular. So that the distribution or non-distribu- 
tion of the Subject depends on the * Quantity ' of the proposi- 
tion, and that of the Predicate on the ' Quality.' 



LESSON VI. 

§ 1. The next thing to be learnt and remembered, is the 
names of the three Terms that occur in a Syllogism. For 
you will have perceived from the foregoing examples, that 
there are always three terms ; which we have designated by 



Lesson vi.] terms of a syllogism. 41 

the Symbols X, Y, and Z. Each Syllogism indeed has, in all, 
three Propositions ; and every Proposition has two Terms ; 
but in a Syllogism each term occurs twice ; as, 'X is Y, Z is 
X; therefore Z is Y.' 

Of these three terms, then, that which is taken as the Sub- 
ject of the Conclusion (' Z ') is called the ' Minor-term ; ' the 
Predicate of the Conclusion ['Y'] is called the ''Major-term ;* 
(from its being usually of more extensive signification than 
the ' Minor,' of which it is predicated) and the Term [' X '] 
which is used for establishing the connexion between those 
two, is thence called the ' Middle-term,^ [or ' medium of proof. '~\ 

Of the two Premises, that which contains the Major-term, 
(' X is Y,') is called the ' Major-premise ; ' (and it is, proper- 
ly, and usually, placed first ; though this order is not essen- 
tial) and that which contains the Minor-term (Z is X) is call- 
ed the ^Minor-premise' tAjid in these two Premises, respect- 
ively, the Major-term and Minor-term are, each, compared 
with the Middle-term, in order that, in the Conclusion, they 
may be compared with each other; that is, one of them 
affirmed or denied of the other. 

§ 2. Now it is requisite, as you will see by looking back to 
the examples formerly given, that, in one or other of the 
Premises, the Middle-term should be distributed. For if each 
of the Terms of the Conclusion had been compared only with 
part of the Middle-term, they would not have been both com- 
pared with the same ; and nothing could thence be inferred. 

Thus, in one of the above examples, when we say ' food ' 
(namely, '■some food,') 'is necessary to life,' the term 'food' 
is undistributed, as being the Subject of a Particular-proposi- 
tion : in other words, we have aflSrmed the term ' necessary to 
life,' of part only, not the whole, of the Class denoted by tlie 
term 'food : ' and again, when we say ' com is food,' the tenu 
food' is again undistributed, (according to the Rule given ia 

the last Lesson) as being the Predicate of an Affirmative : — 
4* 



42 ANALYTICAL INTRODUCTION. Part I. 

in other words, though we have asserted that the term * food ' 
is applicable to * corn,' we have not said (nor, as it happens, is 
it true) that it is not applicaUe to anything else ; so that we 
have not been taking this term * food ' universally, in either 
Premise, but, each time, ' particularly.' And accordingly 
nothing follows from those premises. 

So also, when it is said, * a wise ruler endeavors to civilize 
the People ; and Alfred endeavored to civiHze the People ; ' 
[or ' Y is X, and Z is X,'] the Middle-term is here twice 
made the Predicate of an Affirmative-proposition, and con- 
sequently is left undistributed, as in the former instance; 
and, as before, nothing follows. For, (as was formerly 
observed) we are not authorized to affirm one term of 
another, merely on the ground that there is something which 
has been affirmed of each of them : as the term ' growing ' 
(in the example formerly given) is affirmed of ' vegetables * 
and also of * animals.' 

In each of these cases, then, such an apparent-argument is 
condemned on the ground that it ' has the middle-term undis- 
tributed.^ 

§ 3. The other kind of apparent Syllogism formerly given 
as an example, is faulty (as was then shown) from a different 
cause, and is condemned under a diffisrent title. * Every tree 
is a vegetable ; grass is not a tree, therefore it is not a vege- 
table : ' or, ' every X is Y ; Z is not X ; therefore Z is not Y.' 

Here, the middle-term ' X ' is distributed ; and that, not 
only in one Premise, but in both ; being made, first, the sub- 
ject of a Universal-proposition, and again, the Predicate of a 
Negative. But then, the Major-term, *Y' which has not 
been distributed in the Premise, is yet distributed in the Con- 
clusion ; being, in the Premise, the Predicate of an Affirma- 
tive, and in the Conclusion, of a Negative. We have therefore 
merely compared part of the term [' Y '] * vegetable ' with 
the Middle-term ' Tree ; ' [' X '] and this does not authorize 



Lesson vi.] terms of a syllogism. 43 

our comparing, in the Conclusion, the whole of that same term 
with [Z] ' grass ; ' which, as was explained above, we must 
do, if we deny the term ' grass' of a 'vegetable/ 

Nothing therefore follows from the Premises: for it is 
plain that they would not warrant an affirmative Conclusion. 
To affirm that * grass is a vegetable,' (or, as one might equally 
well, that, ' a house is a vegetable,' because it ' is not a tree,* 
would not have even any appearance of Reasoning. No one 
would pretend to affirm one term of another (as, Y, of Z) on 
the ground that it had been affirmed of something (' X ') 
which had been denied of that other. 

Such a fallacy as the one we have been above considering, 
is condemned as having what is called in technical language, 
an • illicit process ; ' that is, an unauthorized proceeding, from 
a term, w^zdistributed in the Premise, to the same term, dis- 
tributed, in the Conclusion : or, in other words, taking a 
term more extensively in the Conclusion than it had been 
taken in the Premise ; which is, in fact, introducing an ad- 
ditional term. 

§ 4. The examples that have been all along given, both of 
correct-reasoning and of Fallacy, have been, designedly, the 
simplest and easiest that could be framed. And hence, a 
thoughtless reader, observing that the rules given, and the tech- 
nical language employed, though not difficult to learn, are yet 
less easy than the examples themselves to which these are ap- 
plied, may be apt to fancy that his labor has been wasted ; and, 
to say, ' why, common-sense would show any one the sound- 
n(^.ss of the reasoning, or the unsoundness, in such examples 
as these, with less trouble than it costs to learn the rules, and 
the technical terms.' 

And a beginner in Arithmetic might say the same. For, 
the examples usually set before a learner, are, purposely, such 
easy questions as he could answer *in his head' (as we ^^iyy) 
with less trouble than the arithmetical rules cost him. But 



44 ANALYTICAL INTRODUCTION. [_Part I. 

then, by learning those rules, through the means of such sim- 
ple examples, he is enabled afterwards to answer, with little 
difficulty, such arithmetical questions as would be perplexing 
and laborious, even to a person of superior natural powers, 
but untaught. 

It is the same, in the learning of a foreign Language. The 
beginner has to bestow more pains on the translating of a few 
simple sentences, than the matter of those sentences is worth. 
But in the end he comes to be able to read valuable books 
in the Language, and to converse with intelligent foreigners, 
which he could not otherwise have done. 

And so also, in the present case, it will be found that, sim- 
ple as are the examples given, not only all valid Reasoning, 
on whatever subjects, may be exhibited, and its validity shewn, 
in the form that was first put before you, but also, most of the 
Sophistical-arguments, [Fallacies] by which, men are every 
day misled, on the most important subjects, may be reduced 
into the same forms as those of the examples lately given. 

Hume's argument against Miracles, as believed on Testimo- 
ny, which was explained in a former Lesson, is an instance of 
this. And numberless others might be given. 

§ 5. For example, there is an erroneous notion commonly 
to be met with, which is founded on a fallacy that may be thus 
exhibited as a case of undistributed middle-term : * A man 
who is indiiferent about all religion, is one who does not seek 
to force his religion on others ; ' (for though this is far from 
being universally true^ it is commonly believed) ' this man does 
not seek to force his religion on others ; therefore he is indif- 
ferent to all religion.' 

Again, as an example of the other kind of fallacy above- 
mentioned, the ' illicit process ' of the Major-term, we may 
exhibit in that form the sort of Reasoning by which one may 
suppose the Priest and Levite, in the Parable of the good Sa- 
maritan, to have satisfied themselves that the poor wounded 



LiSaon VI.] COMMON FALLACIES. 45 

stranger had no claim on them as a neighbor ; — a kind ol 
procedure of which one maj find instances in real life in all 
times : 

' A kinsman or intimate acquaintance has a claim to our 
neighborly good-offices : this man, however, is not a kinsman, 
&c., therefore he has no claim, &c.' Again 'A Nation which 
freely admits our goods, ought to be allowed freely to supply 
us with theirs : but the French^do not freely admit our goods : 
therefore, &c.' Again, ' Nations that have the use of money, 
and have property in land, are subject to the evils of avarice, 
of dishonesty, and of abject poverty ; but savage nations ha\;e 
not the use of money, &c. &c.' 

And again, ' A kind and bountiful landlord ought to be ex- 
empt from lawless outrage ; but this man is not a kind and 
bountiful landlord ; therefore, &c.' 

It will be found a very useful exercise to select for yourself 
a number of other arguments, good or bad, such as are com- 
monly to be met with in books or conversation, and to reduce 
them to the most regular form they will admit of, in order to 
try their validity by the foregoing rules. 

You must keep in mind, however, (what was said in the first 
Lesson) that technical terms and rules will be rather an in- 
cumbrance than a help, unless you take care not only to un- 
derstand them thoroughly, but also to learn them so perfectly 
that they may be as readily and as correctly employed as the 
names of the most familiar objects around you. 

But if you take the trouble to do this once for all, you will 
find that in the end much trouble will have been saved. For, 
the explanations given of such technical-terms and general 
rules, when thoroughly learnt, once, will save you the necessi- 
ty of going through nearly the same explanation over and over 
again on each separate occasion. 

In short, the advantage of technical terms is just like what 



46 ANALYTICAL INTRODUCTION. \_Part 1 

we derive from the use of any other Common-terms.* When, 
for instance, we have once accurately learnt the definition of 
a ' Circle,' or have had fully described to us what sort of a 
creature an ' Elephant ' is, to say ^ I drew a Circle,' or ' I saw 
an Elephant,' would be sufficiently intelligible, without any 
need of giving the description or definition at full length, over 
and over again, on every separate occasion. 



LESSON vn. 



§ 1. We have seen that all sound Reasoning consists in 
referring that of which we would (in the conclusion) affirm or 
deny something, to a Class, of which that affirmation or denial 
taay be made. Now, * the referring of anything to a Class,' 
means (as you will perceive on looking back to the examples 
that have been given) to affirm of it a Term denoting a Class ; 
which Term, you will have observed, is the Middle-term of 
the Syllogism. 

We are next led, therefore, to inquire what terms may be 
affirmatively predicated of what others. 

It is plain that a proper-name, or any other term that stands 
for a single individual, cannot be affirmed of anything except 
that very individual. For instance, ' Romulus ' — the 
* Thames ' — ' England ' — * the founder of Rome ' — ' this riv- 
er,' &c., denoting, each, a single object, are thence called ' Siur 
gular-terms : * and each of them can be affirmed of that single 
object only, and may, of course, be denied of anything else. 

When we say * Romulus was the founder of Rome,' we 

* This will be more fully explained in the subsequent Lessons. 



Lesson vii.] common-terms4 47 

mean that the two terms stand for the same individual. And 
such is our meaning also when we affirm that ' this river is 
the Thames.' 

On the other hand, those terms which are called * Common ' 
(as opposed to ' Singular ') from their being capable of stand- 
ing for any, or for every, individual of a Class, — such as 
*man,' 'river,' 'country' — may of course be affirmed of 
whatever belongs to that Class : as, ' the Thames is a river ; ' 

* the Rhine and the Ganges are rivers.' 

And observe, that throughout these Lessons we mean bya 

* Class ' not merely a Head or general-description to which 
several things are actually referred, but one to which an indef- 
inite number of things might, conceivahly, be referred ; name- 
ly, as many as (in the colloquial phrase) may ' answer to the 
description.^ .For instance, we may conceive that when the 
first-created man existed alone, some beings of a Superior 
Order may have contemplated him, not merely as a single in- 
dividual bearing the proper-name ' Adam,' but also (by Ab- 
straction, which we shall treat of presently) as possessing 
those attributes which we call, collectively, ' human-nature ; 
and they may have applied to him a name — such as 'Man' — 
implying those attributes [that ^ description,'^ and nothing 
else ; and which would consequently suit equally well any of 
his descendants. 

When therefore anything is said to be ' referred to such and 
such a Class,' we mean either what is, or what might be a 
Class, comprehending any objects that are ' of a certain de- 
scription ; ' which description (and nothing else) is implied by 
the ' Common term,' which is a name of any^ or all, of those 
objects. 

§ 2. A Common-term is thence called (in relation to the 

* Subjects ' to which it is applicable) a ^Predicahle ; ' that is, 
affirmatively-^TQ^\Q,3i^AQ ; from its capability of being affirmed 
of another Term. 



48 ANALYTICAL INTRODUCTION. \^Part T. 

A Singular-term, on the contrary, may be the Subject of a 
proposition, but not the Predicate : unless of a JVegative-^ro- 
position ; (as ' the first-born of Isaac Avas not Jacob ') or un- 
less the Subject and Predicate be merely two expressions for 
the same individual ; as in some of the examples above. 

You are to remember, however, that a Common-term must 
be one that can be affirmed of an indefinite number of other 
terms, in the same sense, as applied to each of them ; as ' veg- 
etable,' to ' grass,' and to an ' oak.' For, different as these 
are, they are both ' vegetables ' in the same sense ; that is, the 
word ' vegetable ' denotes the same thing in respect to both of 
them : [or, ' denotes something common to the two.'] 

But there are several proper-names which are borne, each, 
by many individuals ; such as * John,' ' William,' &c., and 
which are said to be, (in ordinary discourse) very common 
names ; that is, \&cj frequent. But none of these is what we 
mean by a * Common-term ; ' because, though applied to sev- 
eral persons, it is not in the same sense, but always, as denot- 
ing in each case, one distinct individual. 

If I say ' King Henry was the conqueror at Agincourt,' 
and, ' the conqueror of Richard the Third was King Henry,' 
it is not in sense one term, that occurs in both those proposi- 
tions. But if I say, of each of these two individuals, that he 
was a ' King,' the term ' King ' is applied to each of them in 
the same sense. 

§ 3. A Comraon-term, such as ' King,' is said to have sev- 
eral ' Signijicates ; ' that is, things to which it may be applied : 
but if it be applied to every one of these in the same sense, 
[or denotes in each of them the same thing] it has but one 
' signification.^ And a Common-term, thus applied, is said to 
be employed ' univocally.' 

If a term be used in several senses, it is, in meaning, not 
one term only, but several. Thus, when ' Henry ' (or any 
5ther such name) is applied to two individuals to denote, in 



Lesson vii.] common terms. 49 

each case, that ojie distinct person, it is used not as one term, 
but as two ; and it is said to be applied to those two, ' equivo- 
cally.'' 

The like often occurs in respect of Common-terms also ; 
that is, it often happens that one word or phrase, will be not 
merely one but several Common-terms. 

Take, for example, the word ' Case,' used to signify a kind 
of ' covering ; ' and again (in Grammar) an inflection of a 
noun ; (as ' him ' is the accusative [or objective] ca^e of *he') 
and again, a ' case ' such as is laid before a lawyer. This 
word is, in sense, three ; and, in each of the three senses may 
be applied ' univocally ' to several things which are, in that 
sense, signified by it. But when applied to a box and to a 
grammatical case, it is used ' equivocally.' 

§ 4. That process in the mind by which we are enabled to 
employ Common-terms, is what is called ' Generalization ; ' 
Common-terms being often called also ' General-titvms, 

When, in contemplating several objects that agree in some 
point, we ' abstract ' [or draw ojf] and consider separately, 
that point of agreement, disregarding everything wherein they 
differ, we can then designate them by a Common-term, appli- 
cable to them, only in respect of that wliich is ' common ' to 
them all, and which expresses nothing of the differences be- 
tween them. And we obtain in this way either a term de- 
noting the individuals themselves thus agreeing considered in 
respect of that agreement, (which is called a concrete-corsxmon- 
lerm) or again, a term denoting that circumstance itself where- 
in they agree ; which is called an a5s^rac?-common-term. 

Thus we may contemplate in the mind several different 
* kings ; ' putting out of our thoughts the name and individual 
character, of each, and the times and places of their reigns, 
and considering only the regal Office which belongs to all and 
each of them. And we are thus enabled to designate any or 
ivery one of them by the * common ' [or general] term, 
5 



50 ANALYTICAL INTRODUCTION. \_Part I 

'king,' or again, by the term 'royalty' we can express the 
circumstance itself which is common to them. And so in the 
case of any other common-term. 

The 'Abstraction' which here takes place, is so called from 
a Latin- word originally signifying to ' draw off;' because we 
separate, and as it were, draw off, in each of the objects be- 
fore us, that point, — apart from every other, — in which they 
are alike. 

It is by doing this, that ' GeneraHzation ' is effected. But 
the two words have not the same meaning. For though we 
cannot ' generalize ' without ' abstracting , we may perform 
Abstraction without Generalization. 

§ 5. If, for instance, any one is thinking of ' the Sun,' with- 
out having any notion that there is more than one such body 
in the Universe, he may consider it without any reference to 
its place in the sky , whether rising, or setting, or in any other 
situation; (though it must be always actually to some situ- 
ation) or again he may be considering its heat alone, without 
thinking of its light ; or of its Hght alon e ; or of its apparent mag- 
nitn.de, without any reference either to its Hght or heat. Now 
in each of these cases there would be Abstraction ; though 
there would be no Generalization, as long as he was contem- 
plating only a single individual; that which we call the 
' Sun.' 

But if he came to the belief (which is that of most Astro- 
nomers) that each of the fixed Stars is a body affording light 
and heat of itself, as our Sun does, he might then, by abstract- 
ing this common circumstance, apply to all and each of these 
(the Sun of our System, and the Stars) one common-term de- 
noting that circumstance ; calling them all, ' Suns.' And this 
would be, to ' generalize.^ 

In the same manner, a man might, in contemplating a single 
mountain, (suppose, Snowdon) make its hej,ght alone, inde- 
pendently of everything else, the subject of his thoughts ; or 



Lesson vii.] generalization. 



51 



its total hulk ; disregarding its shape, and the substances it is 
composed of; or again, its shape alone; and jet while thus 
abstracting, he might be contemplating but the single mdivi- 
dual. But if he abstracted the circumstance common to 
Snowdon, Etna, Lebanon, &c., and denoted it by the common- 
term ' Mountain,' he would then be said to generalize. He 
would then be considering each, not, as to its actual existence 
as a single individual, but as to its general character, as being 
of such a description as would apply equally to some other 
single objects. 

§ 6. Any one of these Common-terms then serves as a 
'Sign' [or Representative] of a Class; and may be apphed 
to, —that is, affirmed of— all, or any, of the things, it is thus 
taken to stand for. 

And you will have perceived from the above explanations, 
that what is expressed by a Common-term is merely an in- 
adequate — incomplete notion [or ' view ' taken] of an indivi- 
dual. For if, in thinking of some individual object, you re- 
tain in your mind all the circumstances (of character, time, 
place, &c.,) which distinguish it (or which might distinguish 
it) from others, — including the circumstance of unity [or 
singleness] — then any name by which you might denote it, 
when thus viewed, would be a Singular-term ; but if you lay 
aside and disregard all these circumstances, and abstract [con- 
sider separately] merely the points which are common or 

which conceivably might be common — to it with other indi- 
viduals, you may then, by taking this incomplete view [or 
* apprehension '] of it, apply to it a name expressing nothing 
that is peculiar to it; and which consequently wiil equally 
well apply to each of those others ; in short, a Common-term ; 
such as those in the above examples. 

§ 7. You are to remember, then, that there is not, in tlie 
case of these ^ general ' [or common] Terms, (as there is in 
the case of Singidar-tevms) some real thing corresponding to 



52 ANALYTICAL INTRODUCTION. \_Part I. 

each Term, existing independently of the Term, and of which 
that term is merely the 7iame ; in the same manner as Leb- 
anon ' is the name of an actually -existing single individual. 

At first sight, indeed, you might imagine that as any ' in- 
dividual man ' of your acquaintance, or ' Great Britain,' or 
* the Sun,' &c., has an existence in Nature quite independent 
of the name you call it by, so, in like manner, there must be 
some one real thing existing in Nature, of which the Common- 
term ' Man ' or the term ' Island ' is merely the name. 

And some writers will tell you that, this thing, which is the 
subject of your thoughts when you are employing a general- 
term, is, the ' abstract idea ' of Man, of Island, of Mountain, 
&c. But you will find no one able to explain what sort of a 
thing any such ' abstract-idea ' can be : which is one thing, 
and yet not an individual, and which may exist at one and 
the same time in the minds of several different persons. * 

All the obscure and seemingly-profound disquisitions that 
you may perhaps meet with, respecting these supposed ' ab- 
stract ideas ' will but perplex and bewilder you. 

Whether the w^riters of these disquisitions have themselves 
understood their own meaning, we need not here inquire. 
But the simple explanation that has been above given of the 
origin and use of Common-terms, you will be able, with mo- 
derate attention, clearly to understand. And you will find it 
quite sufficient for our present purpose. 

§ 8. You will perceive from it that the subject of our 
thoughts when we are employing a Common-term, is, the 
Term itself, regarded as a ' Sign ; ' namely, a Sign denoting a 

* The question here briefly alluded to, and which could not properly 
be treated of at large in a short elementary work, is that which was at 
one time fiercely contested, throughout nearly all Europe, between the 
•wo rival sects of Philosophers, the Realists and the Nominalists. 

There are several well known works in which the student may find it 
fully discussed. — See Whately's Elements of Logic, B. iv. ch. 5 



Lesson viii.] abstract-ideas. 53 

certain inadequate notion formed [or, view taken] of .'Ru indi- 
vidual which in some point agrees with [or ' resembles 'J some 
other individuals : the notion being, as has been said, ' inade- 
quate ' or ' incomplete,' inasmuch as it omits all peculiarity 
that distinguishes the one individual from the others ; so that 
the same single ' Sign ' may stand equally well for any of 
them. 

And when several persons are all employing and under- 
standing the same Common-term in the same sense, and are 
thence said (as some Writers express it) to have ' one and the 
same Idea ' 43.t once in the mind of each, this means merely 
that they are (thus far) all thinking alike; just as several 
persons are said to be all ' in one and the same posture,^ when 
they have all of them their limbs placed alike ; and to be of 
one and the same complexion when their skins are colored 
alike. 



LESSON VIII. 



§ 1. It has been shown, how, by taking an inadequate 
view of an individual, disregarding every point wherein it 
differs from certain other individuals, and abstracting that 
wherein it agrees with them, we can then employ a Common- 
term, as a sign to express all or any of them : and thnt this 
process is called ' generalization.' 

It is plain that the same process may be further and fur- 
ther extended, by continuing to abstract from each of the 
Classes [or Common-terms] thus formed, the circumstance 
wherein it agrees with some others, leaving out and dis- 
regarding the points of difference ; and thus forming a still 
more general and comprehensive term. 
5* 



5 t ANALYTICAL INTRODUCTION. \_Part I. 

From an Id dividual ' Cedar,' for instance, you may arrive 
in this manner, at the notion expressed by the Common-term 
'■ Cedar,' and thence again proceed to the more general term 
' Tree,' and thence again, to ' Vegetable,' &c. 

And so, also, you may advance from any ' ten ' objects be- 
fore you, (for instance, the fingers ; from which doubtless 
arose the custom of reckoning by tens) to the general-term, — 
the number * ten ; ' and thence again, to the more general- 
term, * number ; ' and ultimately to the term ' quantity.' 

§ 2. The faculty of Abstraction, — at least the ready exer- 
cise of it in the employment of Signs, [Common-terms] seems 
to be the chief distinction of the Human Intellect from that 
of Brutes. These, as is well-known, often display much in- 
telligence of another kind, in cases where Instinct can have 
no place : especially in the things which have been taught to 
the more docile among domesticated animals. But the 
Faculty of Language, such as can serve for an Instrument of 
Reasoning , — that is, considered as consisting of arbitrary 
general Signs, — seems to be wanting in Brutes. 

They do possess, in a certain degree, the use of Language 
considered as a mode of communication : for it is well known 
that horses, and dogs, and many other animals, understand 
something of what is said to them : and some brutes can 
learn to utter sounds indicating certain feelings or perceptions. 
But they cannot, — from their total want, or at least great 
deficiency, of the power of Abstraction — be taught to use 
Ituiguage as an Instrument of Reasoning. 

Accordingly, even the most intelligent Brutes seem in- 
capable of forming any distinct notion of number : to do 
which evidently depends on Abstraction. For, in prder to 
count any objects, you must withdraw yoTir thoughts from all 
differences between them, and regard them simply as units. 
And accordingly, the Savage Tribes (who are less removed 
than we are from the Brutes) are remarked for a great defi- 



Lesson viii.] deaf-mutes. 55 

ciency in their notions of number. Few of them can count 
beyond ten, or twenty : and some of the rudest Savages have 
no words to express any numbers beyond five. 

And universally, it is in all matters where the exercise of 
Abstraction is concerned, that the inferiority of Savages to 
Civilized men is the most remarkable. 

§. 3. That we do, necessarily, employ Abstraction in order 
to reason, you will perceive from the foregoing explanations 
and examples. For you will have observed that there can be 
no Syllogism without a Common-term. 

And accordingly, a Deaf-mute, before he has been taught a 
language, — either the Finger-language, or Reading, — can- 
not carry on a train of Reasoning, any more than a Brute. 
He differs indeed from a Brute in possessing the mental 
capability of employing Language ; but he can no more make 
use of that capability, till he is in possession of some System 
of arbitrary general-signs, than a person born blind from Cat- 
aract can make use of his capacity of Seeing, till the Cataract 
is removed. 

You will find, accordingly, if you question a Deaf-mute who 
has- been taught Language after having grown up, that no 
such thing as a train of Reasoning had ever passed through 
his mind before he was taught. 

If indeed we did reason by means of those ' Abstract-ideas ' 
which some persons talk of, and if the language we used 
served merely to communicate with other men, then, a person 
would be able to reason, who had no knowledge of any arbi- 
trary Signs. But there are no grounds for believing that 
this is possible ; nor, consequently, that ' Abstract-ideas ' (in 
that sense of the word) have any existence at all. 

You will have observed also, from what has been said, that 
the Signs [Common-terms] we are speaking of as necessary 
for the Reasoning-process, need not be addressed to the ear. 
The signs of the numbers, — the figures 1, 2, 3, 4, &c., have 



56 ANALYTICAL INTRODUCTION. \_Part I. 

no necessary connexion with sound; but are equally under- 
stood by the English, French, Dutch, &c., whose spoken lan- 
guages are quite different, 

And the whole of the wrzi(^e?z-language of the Chinese is of 
this kind. In the different Provinces of China, they speak 
different Dialects : but all read the same Characters ; each 
of which (Uke the figures 1, 2, 3, &c.) has a sense quite inde- 
pendent of the sound. 

And to the Deaf-mutes, it must be so mth cdl kinds of 
Language understood by them ; whether Common Writing, 
or the Finger-language.* 

* There have been some very interesting accounts published, by tra- 
vellers in America, and by persons residing there, of a girl named Laura 
Bridgman, who has been, from birth, not only deaf and dumb, but also 
blind. §he has, however, been taught the finger-language, and even to 
read what is printed in raised characters, and also to wiite. 

The remarkable circumstance in reference to the present subject, is, 
that when she is alone, her fingers are generally observed to he moving^ 
though the signs are so slight and imperfect that others cannot make out 
what she is thinking of. But if they inquire of her, she will tell them. 

It seems that, having once learnt the use of Signs, she finds the neces- 
sity of them as an Instrument of thought, when thinking of anything be- 
yond mere indiA'idu&l objects of sense. 

And doubtless every one else does the same; though in our case, no 
one can (as in the case of Laura Bridgeman) see the operation ; nor, in 
general, can it be heai^d ; though some few persons have a habit of occa- 
sionally audibly talking to themselves ; or, as it is called, ' thinking aloud.' 
But the Signs we commonly use in silent reflection are merely mental 
conceptions of uttered words : and these, doubtless, are such, as could be 
hardly at all understood by another, even if uttered audibly. For we 
Tisually think in a kind of short-hand, (if one may use the expression) like 
the notes one sometimes takes down on paper to help the JnemorV; wliich 
consist of a word or two — or even a letter — to suggest a v>-hole sen- 
tence ; so that such notes would be unintelligible to any one else. 

It has been observed, also, that this gui when asleep, and doubtless 
dreaming, has her fingers frequently in motion : being, in fact, talking in 
her sleep. 



LeSS07l VIII.3 HABITS OF ABSTKACTION. 57 

§ 4. Bj the exercise of Abstraction, (it is to be further re- 
marked) we not onlj can separate, and consider apart from 
the rest, some circumstance belonging to every one of several 
individuals before the mind, so as to denote them by a general 
[' common '] term, — and can also, by repeating the process, 
advance to more and more general terms ; — but we are also 
able to fix, arbitrarily, on whatever circumstance we choose to 
abstract, according to the particular purpose we may have in 
view. 

Suppose, for instance, it is some individual ' Building' that 
we are considering : in respect of its materials we may refer 
it to the class (suppose) of ' Stone-buildings,' or of ' wooden,' 
&c., in respect of its use, it may be (suppose) a * house,' as 
distinguished from a Chapel, a Barn, &c., in respect of Orders 
of Architecture, it may be a ' Gothic-building,' or a ' Grecian,' 
&c., in respect of size, it may be a ' large,' or a * small build- 
ing,' in respect of color, it may be * white,' ' red,' ' brown,' &c. 

And so, with respect to anything else that may be the sub- 
ject of our reasoning, on each occasion that occurs. We arbi- 
trarly fix on, and abstract, out of all the things actually exist- 
ing in the subject, that one which is important to the purpose 
in hand. So that the same thing is referred to one Class, or 
to another, (of all those to which it really is referable) accord- 
ing to the occasion. 

For instance, in the example above, you might refer the 
' building ' you were speaking of, to the Class [or Predicable] 
of ' white-hmldimgs,^ — or even of ' vf\Aie.-ohjects,' — if your 
purpose were to shew that it might be used as a land-marl: ; 
if you were reasoning concerning its danger from fire, you 
njight class it (supposing it were oi wood) not only with such 
buildings, but also with hay-stacks and other combustibles : if 
the building were about to be sold, along with, perhaps, not 
only other buildings, but likewise cattle, land, farming imple- 
ments, &c., that were for sale at the same time, the point you 



58 



ANALYTICAL INTRODUCTION. IFart 1. 



would then abstract would be, its being an article of value. 
And so, in other cases. 

§ 5. You thus perceive clearly that we are not to consider 
each object as really and properly belonging to and forming a 
portion of, some one Class only, rather than any other that 
may with truth be affirmed of ifc : and that it depends on the 
particular train of thought we happen to be engaged in, what 
it is that is important and proper to be noticed, and what, 
again, is an insignificant circumstance, and foreign from the 

question. 

But some persons, who have been always engaged in some 
one pursuit or occupation, without attending to any other, are 
apt to acquire a narrow-minded habit of regarding almost 
everything in one particular point of view : that is, consider- 
ing each object in reference only to their own pursuit. 

For mstance, a mere Botanist might think it something 
strange and improper, if he heard an Agriculturalist classing 
together, under the title of ' artificial grasses,' such plants as 
cfover. Tares, and Ryegrass: which, botanically, are widely 
different. And the mere Farmer might no less think it 
strange to hear the troublesome ' weed ' (as he has been used 
to caU it) that is known by the name of ' Couch-grass,' ranked 
by the Botanist as a species of 'wheat,' the ' Triticum 
repens,' the farmer having been accustomed to rank it along 
with ^nettles and thistles,' with which it has no botanical 

connexion. 

Yet neither of these classifications [or ' generalizations 'J 
would be, in itself, erroneous and improper ; though it would 
be improper, in a Work on Natural History to class plants 
according to their agricultural uses ; or, in an Agricultural 
Treatise^ to consider principally (as the Botanist does) tlie 
structure oi i\ie,\Y flowers. 

So also, it would be quite impertinent to take into consi'lera- 
tion a man's learning or ability, if the question were as to the 



Lesson Yiii. habits of abstraction. 59 

allowance of food requisite for his support ; or his stature, if 
you were inquiring into his qualifications as a statesman ; or 
the amount of his property, if you were inquiring into his 
state of health ; or his muscular strength, if the question were 
as to his moral character : though each of these might be im- 
portant in reference to a different inquiry. 

The great importance of attending to these points, you will 
easily perceive by referring to the analysis of Reasoning 
which has been above given. For as the proving of any 
Conclusion consists in referring that of which something is to 
be affirmed or denied, to a Class [or Predicable] of which 
that affirmation or denial can be made, our ability in Reason- 
ing must depend on our power of abstracting correctly, clearly, 
and promptly from t-^e subject in question, that which may 
furnish a * middle-term ' suitable to the occasion. 



PART IL 
COMPENDIUM 



LESSON IX. 



§ 1. We have now gone through, in the way of a slight 
sketch, the Analysis of Reasoning. To analyse (as has been 
already explained) means to ' take to pieces,' so as to resolve 
anything into its elements, [or component-parts.] Thus a 
Chemist is said to ' analyse * any compound substance that is 
before him, when he exhibits separately the simpler substan- 
ces it is composed of, and resolves these again into their 
elements. And when, again, he combines these elements into 
their compounds, and those, again, into further compounds — 
thus reversing the former process (which is called the ' ana- 
lytical ') he is said to be proceeding synthetically : the word 
' Synthesis ' — which signifies ' putting together,' — being tlie 
opposite of ' Analysis.' 

Accordingly, it has been shown in the foregoing Lessons 
that every train of Argument being capable of being ex- 
hibited in a Series of Syllogisms, a Syllogism contains three 
Propositions, and a Proposition, two Terms. And it has been 
shewn how ' Common-terms ' (which are indispensable for 
Reasoning, are obtained by means of Abstraction from Indi- 
vidual objects. 

This analytical method is the best suited for the Jirst intro- 
duction of any study to a learner ; because he there sees, from 
the very beginning, the practical application of whatever is 
taught. But the opposite method — the synthetical — is the 



Lesson ix.] system of rules. 61 

more convenient for storing up in the mind all that is to be 
remembered. 

We shall therefore now go over great part of the same 
ground in a reversed order ; merely referring to such thing.s 
as have been already taught, and adding such further rules, 
and explanations of additional technical-terms, as may be 
needed. 

§ 2. The act of the mind in taking in the meaning 
of a Term, is called, in technical language, the act [or 
' operation '] of * Simple-apprehension ; ' that is * wzere-appre- 
hension,' [or * apprehension-only.'] When a Proposition is 
stated — which consists, as we have seen, of two terms, one 
of which is affirmed or denied of the other, — the ' operation * 
[or ' act '3 of the mind is technically called ' Judgment.' And 
the two Terms are described in technical language, as ' com- 
pared ' together, and as * agreeing ' or as ' disagreeing,' accord- 
ing as you affirm, or deny, the one, of the other. 

When from certain Judgments you proceed to another 
Judgment resulting from them, — that is, when you infer [or 
deduce] a Proposition from certain other Propositions — this 
* operation ' is called ' Reasoning,' or ' Argumentation,' or (in 
the language of some writers) ' Discourse.' 

And these are all the mental operations that we are at pres- 
ent concerned with. 

Each of these operations is liable to a corresponding defect 
namely ' Simple-apprehension ' to indistinctness, ' Judgment/ 
to falsity, and ' Reasoning ' to inconclusiveness ; [or falla- 
cioueness.] And it is desirable to avail ourselves of any 
rules and cautions as to the employment of language, that may 
serve to guard against these defects, to the utmost degree that 
is possible : in other words, to guard, by the best rules we 
-•■ian frame, against Terms not conveying a distinct meaning ; 
— against y^Zse Propositions mistaken for true, — and against 
apparent-arguments [or ' Fallacies ; ' or ' Sophisms '] which 
6 



62 COMPENDIUM. [^Part II. 

are in reality inconclusive, though likely to be mistaken for 
real [valid] arguments. 

And such a System of Rules*, based on a scientific view of 
the Reasoning-process, and of every thing connected with it, 
is what the ancient Greeks, among whom it originated, called 
the ' Dialectic-art ; ' from a word signifying to ' discourse on,' 
or ' discuss ' a subject. 

§ 3. You are to observe, however, two important distinc- 
tions in reference to the above-mentioned defects : 1st, you 
are to remember that which is, really, a Term, may be indis- 
tinctly apprehended by the person employing it, or by his 
hearer ; and so also, a Proposition which is false, is not the 
less a real Proposition : but, on the other hand, any expres- 
sion or statement which does not really prove anything, is not^ 
really, an Argument at all, though it may be brought forward 
and passed off as such. 

2dly. It is to be remembered that (as it is evident from 
what has been just said) no rules can be devised that will 
equally guard against all three of the above-mentioned defects. 

To arrive at a distinct apprehension of everything that may 
be expressed by any Term whatever, and again, to ascertain 
the truth or falsity of every conceivable Proposition, is mani- 
festly beyond the reach of any system of rules. But, on the 
other hand, it is possible to exhibit any pretended Argument 
whatever in such a form as to be able to pronounce decisively 
on its validity or its fallaciousness. 

So that the last of the three defects alluded to (though not 
the two former) may be directly and completely obviated by 
the application of suitable rules. But the other two defects 
can be guarded against (as will presently be shown) only in- 
directly, and to a certain degree. 

* you are to observe that a Science, properly, consists of general truths 
that are to.be known : an Art, of practical rules for something that is to 
be done. 



Lesson ix.] the ' dialectic art.' 63 

In other words, rales may be framed that, will enable us to 
decide, what is, or is not, really a ' Term,' — really, a ' Prop- 
osition,' — or really an ' Argument : ' and to do this, is to guard 
completely against the defect of inconclusiveness ; since nothing 
that is inconclusive, is, really, an 'Argument;' though that 
may be really a ' Term ' of which you do not distinctly appre- 
hend the meaning ; and that which is really a ' Proposition^^ 
may be Si false Proposition. 

§ 4. When two Terms are brought together (or ^ compared,' 
as some express it) as Subject and Predicate of a Proposition, 
they are (as was above remarked) described in technical lan- 
guage, as ' agreeing ' or ' disagreeing,' according as the one is 
affirmed or denied, of the other. 

This ' agreement,' however, does not (you are to observe) 
mean coincidence ; [or that the two terms are ' equivalent '] 
for when I say ' Every X is Y,' or * Every Sheep is a rumi- 
nant-animal,' this does not mean ' X is equivalent to Y ; ' [or 
' X ' and ' Y ' are terms of equal extent~\ indeed we know that 
* ruminant-animal ' is in fact a term of greater extent than 
' sheep ; ' including several other species besides. We only 
mean to assert that it is a Class [or Predicable] comprehend- 
ing under it, at least, the term ' Sheep ; ' but whether it does 
or does not comprehend anything else besides, the proposition 
before us does not declare. 

Hence it is that (as was formerly explained) the Predicate 
of an Affirmative-Y>ropos,\tion is considered as undistributed: 
the Subject being compared with part at least of the Predi- 
cate, and asserted to ' agree ' with it ; but whether there be, 
or h^, not, any other part of the Predicate which does not 
agree with that Subject, is not declared in the proposition 
itself. 

There are, it is to be observed, two apparent exceptions to 
this rule : 1st, the case of a Proposition which gives a Dejini- 
tion of anything ; as when I say ' a triangle is a three-sided 



64 COMPENDIUM. [^Part ii. 

figure ; ' which would not be a correct definition, unless it 
were also true that ' every three-sided figure is a triangle ; ' 
and 2dlj by the case of an affirmative-Proposition, where 
both terms are singular, and denote of course one and the 
same Individual ; as ' Ishmael was the first-born of Abraham.' 

In both these cases the Subject and Predicate are, in each 
proposition, what are called '■ convertible ' [or ' equivalent '] 
terms. But then, to assert or imply both that a certain af- 
firmative-proposition is true, and also that its terms are equiv" 
alent, is to make (as was formerly remarked) not merely one, 
but two assertions. 

Now if I am understood to mean not only that it is true 
that ' a triangle is a three-sided figure,' but also that this is the 
definition of a ' triangle/ then, I am understood as making 
two assertions ; that not only ' every triangle is a three-sided 
figure,' but also that ' every three-sided figure is a triangle.' 
But this is understood not from the Proposition itself, looking 
to the form of expression alone, but from what we know, or 
think, respecting the sense of the Terms themselves, or frcn 
what we suppose the speaker to have intended by those 
Terms. For, all that is implied in the mere form of an 
affirmative-proposition, — as ' X is Y ' — is simply that some 
fart at least of the term ' Y ' (whatever that Symbol may 
stand for,) is pronounced to agree with the term ' X.' 

§ 5. And a like explanation will apply in the other case 
also. If I understand from the sense of the terms in some 
affirmative-proposition, that the Subject and the Predicate 
are each a Singular-term, (denoting, of course, one and the 
same individual) — as ' Ishmael was the first-born of Abra- 
ham,' then I understand, as implied by the meaning of the 
words (though not by the form of the Proposition) another 
proposition also ; namely, that ' the first-born of Abraham was 
Ishmael.' In short, it is from my knowledge of the sense of 
the terms tliemselves that I understand them to be ' convert- 



Lesson ix.] convertible terms. 65 

ible' [or equivalent] terms. For you may observe that a 
Singular-term must, from its own nature, correspond to a 
Common term taken universally, [or, ' distributed J inasmiich 
as it cannot hut stand for the whole (not merely some part) of 
that which it denotes. 

In such cases as the above, then, that which is expressed as 
one proposition, is so understood from the meaning of the 
words as in reality to imply two. And there is, therefore, no 
real exception to the rule, that an Affirmative- proposition 
does not, by the form of the expression, distribute its Predicate. 

§ 6. That which pronounces the agreement or disagreement 
of the two Terms of a Proposition [or which make it affirma- 
tive or negative'] is called, as has been above said, the * Cop- 
ula.' And this is always, in sense, either ' is ' or 'is not.' 
For every Verb, except what is called the ' vSubstantive-verb ' 
to ' be,' contains something more than a bare assertion of the 
agreement or disagreement of two terms. It always contains 
in it the Predicate (or part of the Predicate) also. 

Thus, the proposition 'it rains' (which in Latin would 
be expressed by the single word 'pluit') is resolved 

Subj. Cop. Trcd. 

into ' Rain — is — falling ; ' or in some such way. ' John 

Subj. Cop. 

owes William a pound,' is resolved into ' John — is — 

Prccl. 



owing [or indebted to] William, a pound.' And so in all such 
cases. 

Sometimes, indeed, even the Substantive-verb itself is botli 
Copula and Predicate ; namely, where existence alone is 
affirmed or denied ; as ' God is ; ' ' one of Jacob's sons is not * ; ' 
in which cases 'existing' is the Predicate, 

You are to observe that the Copula has in itself no rela- 
tion to time. If, therefore, anv other ifense besides the Present, 



* Gen. 42. xiii, 
6* 



66 COMPENDIUM. \^Part i. 

of the Substantive-verb, is used, it is to be understood as the 
same in sense with the Present, as far as the assertion is con- 
cerned ; the difference of tense being regarded (as well as the 
person and number) merely as a matter of grammatical pro- 
priety : unless it be where the circumstance of twie really does 
affect the sense of the proposition. And then, this circum- 
stance is to be regarded as part of one of the Terms ; as, ' this 
man was honest ; ' that is, * he is one formerly-honest.^ In 
such a case, an emphasis, wdth a peculiar tone, is laid on the 
word * was.'' 

An Infinitive, you are to observe, is not a Verb, (since it 
can contain no affirmation or denial) but a verbal-noun-sub- 
stantive. And a Participle again, is a verbal-adjective. 

A Participle, or any other Adjective, may be made a Pred- 
icate, but not (by itself) a Subject of a proposition ; as ' this 
grass is green,' * that grass is mown.' 

An Infinitive, though generally placed (in English) at 
the end of a sentence, is almost always (when it is by 
itself a Term) the Subject ; as ' I like to ride ; ' that is? 

Sub. ^ rred. 

* To ride ' [or '■ riding '] is — a thing I like.' 

And observe that there is, in English, an Infinitive in * ing,^ 
the same in sound with the Participle, but different in sense. 
When I say, ^ Riding ' [or ' to ride '] ^ is pleasant,' and again 

* that man is riding,' in the former sentence the word ' riding ' 
is a Substantive, and is the Subject ; in the latter it is an 
Adjective [Participle] and is the Predicate. 

One Infinitive, however, is sometimes predicated of another 
Infinitive ; as, ' seeing is believing ; ' '■ not to advance is to fall 
back ; ' Ho be born is not to be perfected.' 

§ 7. A Term may consist (as was formerly explained) of 
one word, or of several. And care must be taken, when you 
are examining a proposition, not to mistake for one of its 
Terms a word ^\'hich, though it migJit have been used as a 



Lesson ix.] clearness op expression. 67 

Term, is, in that proposition, only a part of a Term. Thus, 
in one of the above examples, the word ^ pound ' is not 
one of the Terms, but only a part of the Term ' owing a 
pound to William.' A description of some object will some- 
times occupy a page or two, and yet be only the Predicate of 
a single Proposition. 

You are to observe also that one single sentence will often 
imply what may be regarded as several distinct Propositions ; 
each indeed implying the truth of the others, but having their 
Terms different, according as we understand the drift (as it 
is called) or design of what is uttered : that is according to 
what we understand the person to be speaking of, (which is 
the Subject) and what it is that he says [predicates] of it. 

1 2 3 4 

Thus ' He — did not — design — your — death ; ' may be 
regarded as any one of at least four different propositions. If 
(No 1) the word ' He ' be marked by emphasis in speaking, 
or by Italics, it will be understood as the Predicate ; and the 
drift of the sentence will be that ' whoever else may have de- 
signed your death, it was not he : ' if the emphasis fall on 
No. 2, the Predicate will be 'designing,' [or 'by design'] 
and the drift of the sentence will be that, ' though he may 
have endangered your life, it was not by design : ' and so with 
the rest. 

. You should endeavor, therefore, so to express yourself as to 
make it clearly understood not only what is the meaning of 
each word you employ, but also what is the general drift of 
the whole sentence : in short, what is the Subject of your 
Proposition, and what it is that you say of it. And, as far as 
you can, you should make this clear by the structure of each 
sentence, without resorting to the expedient of italics or under- 
scoring oftener than is unavoidable. 

There is frequently a great advantage, towards such clear- 
ness, gained, by the English word ' it ' in that sense in which 



68 COMPENDIUM. Impart ii. 

it stands (not as the neuter pronoun, answering to ' He ' and 
* She/ but) as the representative of the Subject of a Proposi- 
tion, of whatever Gender or Number ; so as to allow the Sub- 
ject itself to be placed last : as — 

Subj. Cop. Pred. Subj. 



It — is not — he — that had this design ; ' 



or again — 

Subj. Cop. Pred. Subj. 

'It — is not — by design — that he did this/ &c. 



LESSON X. 



§ 1. A Proposition is, as has been said, an act of judg- 
ment expressed in words ; and is defined to be a * Sentence 
which asserts ; ' or, in the language of some writers, an ' in- 
dicative Sentence:' '•indicative^ [or 'asserting'] meaning 
' that which affirms or denies something.' It is this that dis- 
tinguishes a Proposition from a Question, or a Command, &c. 

Propositions, considered merely as Sentences, are distin- 
guished into ' Categorical ' and ' Hypothetical.' 

The Categorical asserts simply that the Predicate does, or 
does not, apply to the Subject : as ' the world had an intelli- 
gent maker : ' ' Man is not capable of raising himself, unas- 
sisted, from the savage to the civilized state.' The Hypo- 
thetical [called by some writers 'Compound'] makes its 
assertion under a Condition, or with an Alternative ; as ' If 
the world is not the work of chance, it must have had an in- 
telliirent maker:' 'Either mankind are capable of rising into 



Lesson x.] propositions. 69 

civilization unassisted, or the first beginning of civilization 
must have come from above.' 

The former of these two last examples is of that kind called 

* Conditional-propositions * ; ' the ' condition ' being denoted 
by ' if/ or some such word. The latter example is of the 
kind called 'Disjunctive;' the alternative being denoted by 

* either ' and ' or.' 

The division of Propositions into Categorical and Hypo- 
thetical, is, as has been said, a division of them considered 
merely as Sentences: for a like distinction might be extended 
to other kinds of Sentences also. Thus, ' Are men capable 
of raising themselves to civilization ? ' ' Go and study books 
of travels,' are what might be called categorical sentences, 
though not propositions. ' If man is incapable of civilizing 
himself, whence came the first beginning of civilization ? ' 
might be considered as a conditional question ; and ' Either 
admit the conclusion, or refute the argument,' is a disjunctive 
command. 

At present we shall treat only of Categorical Propositions. 

§ 2. It has been above explained that Propositions (of this 
class, — the Categorical) are divided according to their 
' Quantity ' into ' Universal ' and ' Particular : ' — that an 

* IndeJinite-^vo^o%iiion ' is in reality either the one or the 
other ; though the form of expression does not declare which 
is meant : — and also that a ' Singular-T^vo^o&iimn ' is equiva- 
lent to a ' Universal,' since its subject cannot but stand for the 
whole of what that Term denotes, when that whole is one 
single Individual. 

You have also learnt that Propositions are divided, ac- 
cording to their ' Quality,' into ' affirmative ' and ' negative.' 

* Or ' hypothetical,' according to those writers who use the word ' com- 
pound ' where we have used ' hypothetical.' 



70 COMPENDIUM. IPart u. 

The division of them, again, into ^ true ' and ' false ' is also 
called a division according to their * quality ; ' namely, the 
' quality of the Matter : ' (as it has relation to the subject- 
matter one is treating of) while the other kind of quality (a 
proposition's being affirmative or negative) is ' the quality of 
the expression' 

The ' quality of the matter ' is considered (in relation to 
our present inquiries) as accidental, and the ' quality of the 
expression ' as essential. For though the truth or falsity of a 
proposition — for instance, in Natural-history, is the most 
essential point in reference to Natural-history, and of a mathc- 
matical proposition, in reference to Mathematics, and so in 
other cases, — this is merely accidental in reference to an 
inquiry (such as the present) only as to forms of expression. 
In reference to that, the essential difference is between affirm- 
ation and negation. 

And here it should be remarked, by the way, that as, on the 
one hand, every Proposition must be either true or false, so, 
on the other hand, nothing else can be, strictly speaking, either 
true or false. In colloquial language, however, 'true' and 
* false ' are often more loosely applied ; as when men 
speak of the * true cause ' of anything ; meaning, * the real 
cause ; ' — the ' true heir,' that is, the rightful heir ; — a ^ false 
prophet,' — that is, a pretended prophet, or one who utters 
falsehoods ; ' — a ' true ' or ' false ' argument ; meaning a valid 
[real] or an apparent-argviment ; — a man ' true,' or ' false ' to 
his friend ; i. e. faithful or unfaithful &c. 

A Proposition, you are to observe, is Affirmative or Nega- 
tive, according to its Copula ; i. e. according as the Predicate 
is affirmed or denied of the Subject. Thus ' not to advance, 
is to fall back,' is affirmative : ' No miser is truly rich ' [or ' a 
mis( r is not truly rich'] is a negative. 'Afew of the sailors 
were saved,' is an affirmative ; * Pew of the sailors were 



Lesson x.] categorical propositions 71 

saved/ is properly a negative; for it would be understood that 
you were speaking of ' most of the sailors,' and denying that 
they were saved. 

Since then every Proposition must be either Affirmative or 
Negative, and also, either Universal or Particular, Proposi- 
tions are considered as divided (taking into account both 
Quantity and Quality) into four Classes ; which, for brevity's 
sake, are usually denoted by the Symbols A, E, I, ; name- 
ly A. Universal-affirmative, E. Universal-negative, I. Par- 
ticular-affirmative, and O. Particular-negative. 

§ 3. Any two Propositions are, technically, said to be 
'opposed' to each other, when 'having the same Subject 
and Predicate, they differ either in Quantity, or in Quality, 
or in both.' 

In ordinary language, however, (and in some technical 
treatises) propositions are not reckoned as ' opposed ' unless 
they differ in Quality. 

It is evident that with any given Subject and Predicate, 
you may state four distinct Propositions, A, E, I and O : any 
two of which are said to be ' opposed.' And hence there are 
(in the language of most technical writers) reckoned four 
kinds of ' Opposition.' 1st, A and E, — the two Universals, 
Affirmative and Negative, (always supposing the Terms the 
same) are called ' Contraries ' to each other ; 2nd. The two 
Particulars, I and O, ' Suh-contrariesJ 3rd. The two Affirm- 
atives again, or the two Negatives, (A and I, or again, E and 
O) are called ' Subalterns: And 4th, those which differ both 
in Quantity and Quality — as A and O, or E and I, — are 
called * Contradictories: 

It is usual to exhibit in a Scheme (such as that in p. 72) these 
four kinds of ' Opposition ; ' by placing at the corners of a 
Square the Symbols A, E, I, O, as representing, respectively, 
the abovementioned four classes of Propositions. 



72 



n. *. A - - 

i. /. [Every X is Y.J 
c./ 



COMPENDIUM. 

Contraries. 



{^Part II. 



- E. n,/ 

[No X is Y.] i. t. 

c./. 



..^ 





f 
i 


\ 




1 
g 

1 






* 


\ 










^ 


% 










1 ' 


% 




1 






^ 












' 






' 






1 / 




% 








* 










n. t. 


I - - Subcontraries. - - 







n./. 


i./. 


[Some X is Y.] 


[Some 


X is 


not Y.J 


i. t. 


c. t. 




— 






c. «. 



You may substitute for the unmeaning Symbols X, Y, 
(wliicli stand for the Terms of the above Propositions) what- 
ever significant Terms you will; and on their meaning, of 
course, will depend, the truth or falsity of each Proposition. 

For instance, Naturalists have observed that ' animals hav- 
ing horns on the head are universally ruminant ; ' that, of 
* carnivorous animals,' none are ruminant ; and that, of ' ani- 
mals with hoofs,' some are ruminant, and some not. Let us 
take then, instead of ' X,' ' animals with horns on the head,' 
and for ' Y,' * ruminant : ' here, the real connexion of the 
Terms in respect of their meaning — which connexion is called 
the ' matter ' of a proposition — is such that the Predicate may 
be affirmed universally of the Subject ; and of course the 
affirmatives Cwhether Universal or Particular) will be true, 



Lesson VII.] opposition. 



IV, 



and the ' negatives ' fxilse. In this case the ' matter ' is tech- 
nical Ij called ' necessary ; ' inasmuch as we cannot avoid he- 
lieviug the Predicate to be applicable to the Subject. 

Again, let ' X ' represent carnivorous animal/ and ' Y ' 

* ruminant ; ' this is a case of what is called ' impossible mat- 
ter ; ' (e. e. where we cannot possihly conceive the Predicate 
to be applicable to the Subject) being just the reverse of the 
foregoing ; and, of course, both the Affirmatives wall here be 
false, and both Negatives true. 

And, lastly, as an instance of what is called ' contingent 
matter,' — i. e. where the Predicate can neither be affirmed 
universally, nor denied universally, of the Subject, take 

* hoofed animal ' for ^ X ' and < ruminant * for ' Y ; ' and of 
course the Universals will both be false, and the Particulars 
true : that is, it is equally true that ' some hoofed animals are 
ruminant,' and that ' some are not.' 

§ 4. You will perceive, then, on examining such a Scheme, 
that ' Contrary ' Propositions can never be both of them true, 
though they may (viz. : in ' contingent-matter '] be both false : 
that ' AS'wScontraries,' on the other hand, may be both true, but 
never both false : that ' Contradictories ' [diametricaUy-op^o- 
site Propositions] must in every case be, one true, and the 
other false : and that * Subalterns ' (of which the Universal is 
called the ' Suhalternant, and the Particular the * Subalter- 
nate ') may be either both true, or both false, or the one true 
and the other false. 

These last Propositions, however, though reckoned, as has 
been said above, by most dialectical writers, among those op- 
posed, are not so accounted in ordinary discourse. 

The four kinds of Propositions, A, E, I, O, have been, in 

the Scheme, marked, each, with the letters ^ for 'true' and 

/ for ' false,' and also with the letters n, ^, c, to denote the 

three kinds of matter, (necessary, impossible, contingent.) in 

7 



74 COMPENDIUM. \^PaH II. 

order to point out i&hich propositions are true, and which, 
false, in each kind of matter. 

The technical terms we have here explained, are needful 
to be learnt, as being, some of them, in frequent use, and as 
being convenient for the avoiding of circumlocution and of 
indistinctness. 

* Contradictory-opposition ' is the kind most frequently al- 
luded to, because (as is evident from what has been just said) 
to deny, — or to disbelieve, — a proposition, is to assert, or to 
believe, its Contradictory ; and of course, to assent to, or main- 
tain a proposition, is to reject its Contradictory. Belief, 
therefore, and Disbelief, are not two different states of the 
mind, but the sa7ne, only considered in reference to two Con- 
tradictory propositions. And consequently. Credulity and 
Incredulity are not opposite habits, but the same ; in refer- 
ence to some class of propositions, and to their contradictories. 
For instance, he who is the most incredulous respecting a 
certain person's guilt, is, in other words, the most ready to 
believe him not guilty ; he who is the most credulous * as to 
certain works being within the reach of Magic, is the most 
incredulous [or ' slow of heart to believe '] that they are not 
within the reach of Magic ; and so, in all cases. 

The reverse of believing this or that individual proposition 
is, no doubt, to disbelieve that same proposition ; but the v&- 
verse oi" belief generally, is (not belief; since that implies be- 
lief; but) doubt. 

And there may even be cases in which doicbt itself may 
amount to the most extravagant credulity. For instance, if \ 
any one should ' doubt whether there is any such Country as 
Egypt,' he would be in fact believing this most incredible 
proposition ; that ' it is possible for many thousands of persons, 
unconnected with each other, to have agreed, for successive 



* As the Jews, in the time of Jesus, in respect of his works. 



I 



Lesson x.J simple-conversion. 75 

Ages, in bearing witness to the existence of a fictitious Coun- 
try, without being detected, contradicted, or suspected.' 

All this, though self-evident, is, in practice, frequently lost 
sight of. 

§ 5. A Proposition is said to be ' convejied,' when its 
* Terms are transposed ; ' i. e., when the Subject is made the 
Predicate, and the Predicate the Subject. And when no 
other change is made, this is called 'simple conversion.' 
When for instance I say ' no carnivorous animal is a rumi- 
nant,' the ' sim^lQ-converse ' of this would be, ' no ruminant is 
a carnivorous animal.' 

The ' conversion ' of such a proposition as this, ' No one 
[is happy who] is anxious for change,' would be effected by 
altering the arrangement of the words in brackets, into ' who 
is happy.' 

The Conversion of a Proposition is said to be ' illative,' 
when the truth of the ' Converse ' is ' implied ' (looking mere- 
ly to the form of expression) ' by the truth of the original 
proposition : ' [or ' exposita '] which is the case in the exam- 
ple above : it being evident that if the former of those Propo- 
sitions (whatever may be the meaning of the Terms) be true, 
the Converse must be true also. For to say that ' No X is Y,' 
is to imply that ' no Y is X.' 

You are to observe, however, that the Converse of a 
true Proposition may happen to be true also, without the 
Conversion's being ' illative ; ' that is, when the truth of that 
Converse is not implied by the truth of ihe ' Exposita ' [the 
original proposition]. Thus, ' Every X is Y ' does not imply 
that ' every Y is X,' though it ipay happen that both proposi- 
tions may be true. 

For instance, that ' Every tree is a vegetable,' does not 
imply that ' Every vegetable is a tree ; ' and this last hap- 
pens in fact to be not true. But no more is it implied, when 
I say, ' every equilateral triangle is equiangular,' that ' every 



76 COMPENDIUM. [^Part ii. 

equiangular triangle is equilateral ; ' for though both these 
propositions are true, the one of them does not imply the other ; 
and they are separately demonstrated as distinct propositions, 
in geometrical treatises. 

In order to understand why the simple-conversion of ' every 
X is Y/ into ' every Y is X,' is not ' iUative,' you have only 
to observe that, in the * Exposita,' [original proposition] ' Y 
is undistributed, as being the predicate of an .Affirmative ; 
while, in the ' Converse,' it is ' distributed,' by being made the 
Subject of a Universal. A new Term is therefore, in fact, 
introduced ; since instead oi part of the Term ' Y ' we have 
employed the whole of it ; and the agreement or disagreement 
of one Term with some 'part of another Term, does not imply 
its agreement or disagreement with every part of it ; that is, 
with the whole. For though a part is implied by a whole, a 
whole is not implied by a part. 

When, for instance, I say ' every tree is a vegetable ' I 
am employing (as was formerly explained) the Term ' vegeta- 
ble ' to stand only for part of its ' significates ; ' and this does 
not authorize me to employ it (in the Converse) as standing 
for all its Significates ; as in saying that ^ every vegetable is a 
tree.' 

And strictly speaking, that is not a real ' conversion,' — but 
only an * apparent conversion,' — which is not ' illative.' For, 
(as has been above said) there is not a mere transposition of 
the terms, but a new term introduced, when a term which was 
undistributed m the ' exposita,' is distributed [taken univer- 
sally] in the Converse. 

But as it is usual, in common discourse, to speak of ' an 
unsound argument,' — meaning, ' an apparent-dJ^guTHQTii, which 
is in reality not an argument,' so, in this case also, it is com- 
mon to say, for instance, that ' Euclid proves first that all 
equilateral triangles are equiangular, and afterwards he proves 
the Converse, that all equiangular triangles are equilateral ; 



Lesson x.] illative-cojsvkrsion. 77 

or again, to say, ' It is true that all money is wealth ; but I 
deny the Converse, (in reality, the apparent-conY^rsQ) that all 
wealth is money.' 

§ 6. Conversion, then, strictly so called, — that is, ' illa- 
tive-conversion,' — can only take place when no term is dis- 
tributed in the Converse, which was undistributed in the 
* Exposita.' 

Hence, since E [a Universal-negative] distributes both 
terms, and I, [a Particular-affirmative] neither, these may 
both be simply-converted illatively. As in the example 
above, ' no carnivorous animal is ruminant,' implies by the 
very form of the expression, that ' no ruminant is a carnivo- 
rous animal.' And so also ' some things which are strange 
are believed,' implies that ' some things which are believed 
are strange.' 

We may also illatively-convert A [a Universal-affirmative] 
by altering its ' Quantity ' from Universal to Particular. 
For ' Every X is Y ' does imply that ' some Y ' (though not 
that '■every Y') 'is X.' So in the example above we might 
allowably have stated (though not that ' all vegetables,' yet) 
that ' some vegetables are trees.' 

This procedure is called ' conversion by limitation : ' or 
according to some writers, ' conversion per accidens.' And it 
may be applied to E also ; as, for instance, in the example 
above, you might have said ' Some ruminant is not carnivo- 
rous ; ' though this would have been to come short of what 
you were warranted in stating. 

But in O [particular-negative] the conversion will not be 
illative, on account of the rule that the Predicate of a Nega- 
tive is always distributed. The proposition, therefore, * Some 
X is not Y' does not imply that ' some Y is not X ; ' since X 
is distributed in the ' Converse ' and was not, in the ' Ex- 
posita,' in which it was the Subject of a Particular. It is true 
7* 



78 



COMPENDIUM. [Fart II. 



that 'some men are not negroes:' but, this does not imply 
that ' some negroes are not men.' 

A Particular negative [0] cannot be converted illatively, 
except by changing its Quality from negative to affirmative, 
(without altering the sense) by regarding the negation as 
attached to the Predicate instead of to the Copula. Thus 

<SomeX is^'not Y' may be taken as an affirma- 

S. Cop. Fr. 1 1 . 1 

tive, namely, ' Some X is not Y ; ' and this latter 

proposition [I] may of course be simply-converted illatively ; 

S. Cop. P.^ 

as ' Some not Y is ^' 

Thus, ' Some men are not-negroes ' implies that * Some who 
are not negroes are men ; ' or (as such a proposition is ^often 
expressed) ' One may be a man without being a negro.' So 
again ' Some who possess wealth are not happy,' implies that 
< Some who are not-happy possess wealth.' 

§ 7. This procedure is technically called ' Conversion-by- 
negation; [or, by ' Contraposition.'] It is applicable also t» 
[A] Universal-affirmatives. For, to affirm some Predicable 
of a Subject, or [to assert the presence of some attribute] is the 
same thing in sense as to deny its absence. Hence a Univer- 
sal-affirmative may be stated as a JJmYevsal-negative ; which 
(as we have seen) may be simply-converted. 

Thus Every ' X is Y ' is equipollent [or equivalent in sense'] 
to ' No X is not Y ; ' which may be illatively converted into 
* nothing that is not Y — is — X : ' or ' whatever is not Y 

is not — X.' 

So the proposition, ' Every true poet is a man of genius,^ 
may be stated as ' No true poet-is — not-a-man-of-genius ; ' 
which (being E) may be illatively converted into 'no one 
who is not a man of genius is a true poet : ' (as such a propo- 
sition is very commonly expressed) ' None but a man of 
genius can be a true poet ; ' or again, ' a man of genius alo7ie 



Lesson x.] conversion-bt-negation. 79 

can be a true poet ; ' or again, ' One cannot be a true poet 
without being a man of genius.' 

And here it is worth remarking, by the way, that in such 
examples as the above, the words ' may,' ' can,' ' cannot,' &c. 
have no reference (as they sometimes have) to power, as ex- 
ercised by an agent ; but merely to the distribution or non- 
distribution of Terms : or to the confidence or doubtfulness we 
feel respecting some supposition. 

To say, for instance, that ' a man who has the plague may 
recover,' does not mean that ' it is in his power to recover if 
he chooses ; ' but it is only a form of stating a particular- 
proposition : [I] namely, that ' Some who have the plague 
recover.' And again to say, ' there may be a bed of coal in 
this district,' means merely, ' The existence of a bed of coal 
in this district — is — a thing which I cannot confidently deny 
or affirm.' 

§ 8. So also to say ' a virtuous man cannot betray his 
Country ' [or ' it is impossible that a virtuous man should be- 
tray &c.'] does not mean that he lacks the power, (for there 
is no virtue in not doing what is out of one's power) but 
merely that ' not betraying one's country ' forms an essential 
part of the notion conveyed by the term ' virtuous.' We 
mean, in short, that it is as much out of our power to conceive 
a virtuous man who should be a traitor, as to conceive ' a 
Square with unequal sides ; ' that is, a square which is not a 
square. The expression, therefore, is merely a way of 
stating the Universal-proposition [E] ' No virtuous man be- 
trays his Country.' 

So again, to say, ' a weary traveller in the deserts of 
Arabia must eagerly drink when he comes to a Spring,' does 
not mean that he is compelled to drink, but that / cannot 
avoid believing that he will ; — that there is no doubt in my 
mind. 

In these, and many other such instances, the words ' may,' 



80 COMPENDIUM. [^Parf u. 

* must,' ' can/ ' impossible,' &c. have reference, not to power 
or absence of power in an agent, but only to universality or 
absence of Universality in the expression ; or, to doubt or 
absence of doubt in our own mind, respecting what is asserted. 



LESSON XI, 



§ 1. An Argument [or Act of Reasoning expressed in 
words] is defined ' an Expression in which, from something 
laid down [assumed as time] something else is concluded to 
be true, as following necessarily [resulting] from the other.' 
That which follows from the other, is called (as was formerly 
explained) the ' Conclusion ; ' and that from which it follows, 
the ' Premises ; ' or in the language of some writers, the * An- 
tecedent.' *^ 

The above is the strict technical definition. But in ordi- 
nary language the word ' Argument' is often employed to de- 
note the Premises alone ; or, sometimes that one of the 
Premises which is expressed, when the other is understood: 
as when one speaks of proving so and so hy this or that argu- 
ment ; meaning, by such and such a Premise. 

And you may observe, by the way, that of the two 
Premises, the Major (formerly explained) is, in common dis- 
course, often called the ' Principle,' and the Minor-premise, 
the * Reason.' 

Frequently also in common discourse * an Argument ' is used 
to signify a ' Series of arguments,' leadhig ultimately to the 
Conclusion maintained. 

An Argument, if stated in such a regular form that ' its 
conclusiveness [its being really an Argument"! is appai'ent 



Lesson xi.] an argument defined. 



81 



from the mere form of expression alone; (independently of 
the meaning of the words) is then called a ' Syllogism.' As, 
' Every X is Y* ; Z is X, therefore Z is Y ; ' in which, ai 
was formerly explained, the truth of the Conclusion, — assum- 
ing the Premises to be true, — must be admitted, whatever 
Terms you may make X, Y, and Z, respectively, stand for. 

You are to remember, therefore, that a Syllogism is not 
(as some have imagined) a peculiar kind of argument ; but 
only a certain form m which every Argument may be ex- 
hibited. 

§ 2. One circumstance which has tended to mislead persons 
as to this point, is, that in a Syllogism we see the Conclusion 
following certainly [or necessarily] from the Premises; and 
again, in any apparent-syllogism which on examination is 
found to be (as you have seen in some of the examples) not a 
real one [not ' valid '] the Conclusion does not follow at all; 
and the whole is a mere deception. And yet we often hear 
of Arguments which have some weight, and yet are not quite 
decisive ; — of Conclusions which are rendered probable^ but 
not absolutely certain &c And hence some are apt to im- 
agine that the conclusiveness of an argument admits of de- 
grees ; and that sometimes a conclusion may, prohaUy and 
'partially^ — though not certainly and completely — follow from 
its Premises. 

This mistake arises from men's forgetting that the Premises 
themselves will very often be doubtful ; and then, the conclu- 
sion also will be doubtful. 

As was shewn formerly, one or both of the Premises 
of a perfectly valid Syllogism may be utterly false and ab- 
surd : and then, the Conclusion, though inevitably following 
from them, may be either true or false, we cannot tell which. 
And if one or both of the Premises be merely probable, we 



* See above. Lesson IX. § 4. 



82 COMPENDIUM. [^Part II. 

can infer from them only a probable conclusion ; though the 
conclusiveness, — that is, the connexion between the Premises 
and the Conclusion — is perfectly certain. 

For instance, assuming that ' every month has 30 days ' 
(which is palpably false) then, from the minor-premise that 
' April is a month,' it follows (which happens to be true) that 
April has 30 days : ' and from the minor-premise that ' Feb- 
ruary is a month ' it follows that ' February has 30 days ; ' 
which is false. In each case the conclusiveness of the Argu- 
ment is the same ; but in every case, when we have ascer- 
tained the falsity of one of the Premises, we know nothing. (as 
far as that argument is concerned) of the truth or falsity of the 
Conclusion. 

§ 3. When, however, we are satisfied of the falsity of some 
Conclusion, we may, of course, be sure that (at least) one of 
the Premises is false ; since if they had both been true, the 
Conclusion would have been true. 

And this — which is called the ' indirect ' mode of proof — 
is often employed (even in Mathematics) for establishing what 
we maintain : that is, we prove the falsity of some Proposi- 
tion (in other words, the truth of its contradictory) by showing 
that if assumed, as a Premise, along with another Premise 
known to be true, it leads to a Conclusion manifestly false. 
For though, from a false assumption, either falsehood or 
truth- may follow, from a true assumption, truth only can 
follow. 

Let us now look to the case of a doubtful Premise. Sup- 
pose it admitted as certain that ' a murderer deserves death,' 
and as 'probable that ' this man is a murderer,' then, the Con- 
clusion (that ' he deserves death ') is probable in exactly the 
same degree. 

But though when one Premise is certain, and the other, 
only probable, it is evident that the Conclusion will be exactly 
as probable as the doubtful premise, there is some liability to 



Lesson xi.] degrees of probability. 83 

mistake, in cases where each Premise is merely probable. 
For though almost every one would perceive that in this case 
the probability of the Conclusion must be less than that of 
either Premise, the precise degree in wliich its probability is 
diminished, is not always so readily apprehended. 

And yet this is a matter of exact and easy arithmetical cal- 
culation. I mean, that, given the probability of each Premise, 
we can readily calculate, and with perfect exactness, the 
probability of the Conclusion. 

As for the probability of the Premises themselves that are 
put before us, that, of course, must depend on our knowledge 
of the subject-matter to which they relate. But supposing it 
agreed what the amount of probability is, in each Premise, 
then, we have only to state that probability in the form of a 
fraction, and to multiply the two fractions together ; the 
product of which will give the degree of probability of the 
Conclusion.* 

§ 4. Let the probability, for instance of each Premise be 
supposed the same ; and let it, in each, be f ; [that is, let 
each Premise be supposed to have two to one in its favor ; 
that is, to be twice as likely to be true as to be false] then the 
probabihty of the Conclusion will be two thirds of two thirds ; 
that is I" ; — rather less than one half. For since twice two 
is four, and thrice three nine, the fraction expressing the 
probability of the Conclusion will be four ninths. 

For example, suppose the Syllogism to be * A man who has 
the plague will die of it ; ' (probably) ' this man has the 
plague ; ' (probably) therefore, (probably) ' he will die of it.' 
We are — suppose — not certain of either Premise ; though 

* Those who are at all familiar with Arithmetic will hardly need to be 
reminded that, — since a fraction is less than a unit, — what is called (not 
strictly, but figuratively) rmdtiphpvg any thing by a fraction, means, tak- 
ing it less than once ; so tliat, for instiince, g-f-§- that is a half multiplied 
(as it is called) by two-thirds, means two-thu'ds of a half; i. e. 2 or ^. 



84 COMPENDIUM. l^Part ii. 

we think each to be probable : we have judged — suppose — 
that of 9 persons with the symptoms this man exhibits, two 
thirds, — that is, six — have the plague : and again, that two 
thirds of those who have the plague — that is, four oivt of six 
— die of it : then, of 9 persons who have these symptoms, 4 
may be expected to die of the plague. 

Again ' Every X is Y ; f Z is X f , therefore Z is Y ' 
{j-j=^) let the fractions written after each Premise express 
the degree of its probability ; and the result will be that which 
is given as the probability of the Conclusion. 

For instance, * A Planet without any atmosphere is unin- 
habited : the moon is a planet without any atmosphere ; 
therefore, the moon is uninhabited : ' supposing these Propo- 
sitions to be those represented in the former example (of X, 
Y, and Z) then the probability that ' the moon is uninhabited,* 
will be two thirds of three fourths ; or one half; since f mul- 
tiplied by three fourths gives t2'^2"-* 

In the examples just given, you will observe that the 
probability of each Premise has been supposed more than ^ ; 
that is, each has been assumed to be more likely to be true 
than not ; and yet there is, for one of these Conclusions, only 

* Some persons profess contempt for all such calculations, on the 
ground that we cannot be quite sure of the exact degree of probability of 
each premise. And it is true that we are, in most cases, exposed to this 
unavoidable source of uncertainty ; but this is no reason why we should 
not endeavor to guard against an additional uncertainty, which can be 
avoided. It is some advantage to have no more doubt as to the degree 
of probability of the Conclusion, than we have in respect of the Premises. 

And in fact there are offices, kept by persons whose business it is, in 
which calculations of this nature are made, in the purchase of contingent- 
reversions, depending, sometimes, on a great variety of risks which can only 
be conjecturally estimated, and in effecting Insurances, not only ajiainst 
ordinary risks (the calculations of which are to be draAAm from stati>^tical- 
tables) but also against every variety and degree of cx^m-ordinaiy risks ; 
the exact amount of which no one can confidently pronounce upon. But 
the calculations are based on the best estimate that can be formed. 



Lesson xi.] degrees of probability. 85 

an even chance ; and for the other less. The supposed pa- 
tient is supposed to be rather less likely to die of the plague 
than not. 

And of course when there is a long train of reasoning, — 
the Conclusion of each argument being made one of the 
Premises of a succeeding one, — then, if a number of merely- 
probable Premises are introduced, the degree of probability 
diminishes at each successive stage. 

And hence it may happen, in the case of a very long train 
of reasoning, that there may be but a slight probability for the 
ultimate Conclusion, even though the Premises successively 
introduced, should be, some of them, quite certain, and the 
rest, more probable than not. 

And hence, we often have to employ several distinct trains 
of arguments, each tending separately to establish some degree 
of probability in the Conclusion. 

§ 5. When you have two (or more) distinct arguments, 
each, separately, establishing as probable, the same conclu- 
sion, the mode of proceeding to compute the total probability, 
is the reverse of that mentioned just above. For, there, — in 
the case of two probable premises, — we consider what is the 
probability of their being both true ; which is requisite in 
order that the conclusion may be established by them. But 
in the case of a conclusion twice (or oftener) proved probable, 
by separate arguments, if these distinct indications of truth 
do not all of them fail, the conclusion is established. You 
consider, therefore, what is the probability of both these indi- 
cations of truth being combined in favor of any conclusion that 
is not true. 

Hence the mode of computation is, to state (as a fraction) 
the chances against the conclusion as proved by each argu- 
«nent ; and to multiply these fractions together, to ascertain 
the chances against the conclusion as resting on both the 
arguments combined ; and this fraction being subtracted from 
8 



86 COMPENDIUM. \^Part ii. 

unity, the remainder will be the probability /or the conclusion. 

For instance, let the probability of a conclusion as estab- 
lished by a certain argument be ^ : (suppose, that this man 
is the perpetrator of a certain murder, from stains of blood 
being found on his clothes) and again,, of the same conclusion 
as established by another argument, |- : (suppose, from the 
testimony of some witness of somewhat doubtful character) 
then, the chances against the conclusion in each case, respect- 
ively, will be 1^ and -| ; which multiplied together give ^ or 
^ against the conclusion. The probability, therefore, jTor the 
conclusion as depending on these two arguments jointly (i. e. 
that he is guilty of the murder) will be f, or two to one.* 

As for the degree of probability of each Premise, that, as 
we have said, must depend on the subject-matter before us ; 
and it would be manifestly impossible to lay down any fixed 
rules for judging of this. But it would be absurd to complain 
of the want of rules determining a point for which it is plain 
no precise rules can be given ; or to disparage, for that reason, 
such rules as can be given for the determining of another 
point. Mathematical Science will enable us — given, one side 
of a triangle and the adjacent angles, — to ascertain the other 
sides ; and this is acknowledged to be something worth learn- 
ing, although mathematics will not enable us to answer the 
question which is sometimes proposed in jest, of ' how long 
is a rope ? ' 

Men are often misled in practice by not attending to these 
circumstances, plain as they are, when pointed out. 

§ 6. It has been already explained that the Maxim [or 
Dictum] applicable to every Argument when stated in the 
clearest form, is, that ' whatever is predicated universally of 
any term, may be predicated in like manner [affirmed, or de- 
nied, as the case may be] of whatever is comprehended under 

* Sec Lesson XVIL, § 10. 



Lesson xi.] universal principle of reasoning. 87 

that term : ' and that this, consequently, is the ' Universal 
Principle ' of Reasoning. 

And you may observe that this Dictum [or Maxim] may 
in fact be regarded as merely the most general statement of 
' An Argument' — not, this, or that individual argument ; but 
any and every ' Argument, abstractedly.' 

For instance, if you say ' this man is contemptible because 
he is a liar,' you evidently mean to be understood, ' every 
liar is contemptible ; this man is a liar ; therefore he is con- 
temptible.' Now if you so far generalize this Syllogism as to 
omit all consideration of the very terms actually occurring in 
it, ahstracting, and attending solely to, the jTorm of expression, 
you vi^ill have ' Every X is Y ; Z is X ; therefore Z is Y,' 
and then if you proceed to make a still further abstraction, 
saying, — instead of ' Every X ' — ' any-term-distrihuted^ and 
instead of * Y ' — ' anything whatever affirmed of that term,' 
and so on, you will have, in substance, the very ' Dictum ' 
we have been speaking of: which may be separated into 
three portions, corresponding to the three Propositions of a 
Syllogism : thus, 

1. 'Anything whatever' (as *Y') affirmed of a whole 
class (as ' X ') 

2. under which class something else (as Z) is compre- 
hended, 

3. may be affirmed of that (namely ^ Z ') which is so com- 
prehended ; ' 

These three portions into which the Dictum has been sepa- 
rated, evidently answer to the Major-premise, Minor-premise, 
and Conclusion, of the Syllogism given above. And it is 
plain that the like explanation will apply (if ' denied ' were 
put for ' affirmed ') to a Syllogism with a negative conclusion. 
So that the ' Dictum ' is, in fact, as we have said, merely the 
most abstract and general form of stating the Act of Reason- 
ing^ universally. 



88 COMPENDIUM. \^Part II. 

§ 7. Some persons have remarked of this ' Dictum ' (mean- 
ing it as a disparagement) that it is merely a somewhat cir- 
cuitous explanation of what is meant hy a Class. It is, in 
truth, just such an explanation of this as is needful to the 
student, and which must be kept before his mind in reasoning. 
For you are to recollect that not only every Class [the Sign 
of which is, a ' Common-term '] comprehends under it an in- 
definite number of individuals — and of other Classes — dif- 
fering in many respects from each other, but also most of those 
individuals and classes may be referred, each, to an indefinite 
number of classes (as was formerly explained) according as 
we choose to abstract this point or that, from each. 

Now to remind one, on each occasion, that so and so is re- 
ferable to such and such a Class, and that the Class which 
happens to be before us comprehends such and such things, 
— this, is precisely all that is ever accomplished hy Reasoning. 

For you may plainly perceive, on looking at any of the 
examples above, that when you assert both the Premises taken 
in conjunction, you have, virtually, implied the Conclusion. 
Else, indeed, it would not be impossible, (as it is) for any one 
to deny the Conclusion, who admits both Premises. 

§ 8. Hence, some have considered it as a disparagement to 
a Syllogism (which they imagine to be one hind of Argument) 
that you can gain no new truth from it ; the Conclusions it 
establishes being in fact known already, by every one who 
has admitted the Premises. 

Since, however, a Syllogism is not a certain distinct kind 
of argument, but any argument whatever, stated in a regular 
form, the complaint, such as it is, lies against Reasoning alto- 
gether. 

And it is undeniable that no new truthy — in one sense of 
the word — (and that, perhaps, the strictest sense) can ever 
be established by Reasoning alone ; which merely unfolds, as 
It were, and develops, what wa>, in a manner, wrapped up 



Lesson xi.] information and instruction. 89 

and implied in our previous knowledge ; but which we are 
often as much unaw^are of, to all practical purposes, till brought 
before us, as if it had been wholly beyond our reach. 

New truths, — in the strictest sense of the word — that is, 
such as are not implied in anything that was in our minds be- 
fore, — can be gained only by the use of our senses, or from 
the reports of credible narrators, &c. 

An able man may, by patient Reasoning, attain any amount 
of mathematical truths ; because these are all -implied in the 
Definitions. But no degree of labor, and ability, would give 
him the knowledge, by ' Reasoning ' alone, of what has taken 
place in some foreign country ; nor would enable him to know, 
if he had never seen, or heard of, the experiments, what would 
become of a spoonful of salt, or a spoonful of chalk, if put into 
water, or what would be the appearance of a ray of Hght when 
passed through a prism. 

§ 9. These two modes of arriving at any truth are per- 
ceived by all men as distinct. And they are recognized in 
the expressions in common use. The one is usually called 
* information ; ' the other ' instruction* ^ We speak of trust- 
ing to the information (not, the instruction) of our senses. 
Any one who brings news from any place, or who describes 
some experiments he has witnessed, or some spot he has vis- 
ited, is said to aflbrd us information. 

A Mathematician again, a Grammarian, — a Moralist, — 
any one who enters into a useful discussion concerning human 
life, — any one in short who satisfactorily proves anything to 
us by reasoning, — is said to afford us instruction. 

And in conversing with any one who speaks judicious^ly, 
dne sometimes says ' very true ! ' or ' that is a very just remark : 
that never struck me before, &c.' In these and suchlike ex- 
pressions, we imply both that wliat he says is not sttperflxous., 

* It is not meant that this is the only sense of these words. 



90 



COMPENDIUM. \_Part II. 



but valuable and important, and also that we are conscious of 
having ourselves possessed, in our own previous knowledge, 
the germ of what he has developed, and the means of ascer- 
taining the truth of what he has said ; so as to have a right to 
bear our- testimony to it. 

But when any one gives us information about a foreign 
Country, &c. though we may fully helieve him, and be inter- 
ested by what he tells us, we never think of saying 'very 
true ! ' or ' you are quite right.' We readily perceive that in 
this case the knowledge imparted is new to us in quite another 
sense ; and is what no reasoning alone could have imparted; 
being not implied in anything we knew already. 

These two modes of attaining what are, in different senses, 
new truths, (and which of course, are often mixed together) 
may be illustrated by two different modes in which a man may 
obtain an addition to his wealth. One man, suppose, has 
property to a certain value, bequeathed to him: another dis- 
covers on his estate a mine of equal value. Each of these 
is enriched to the same degree. But the former of them ac- 
quires what he had, before, no rigU to; the latter merely 
comes to the knowledge and use of that which was, before, 
legally, his property ; though, till discovered, it brought him 

no advantage. 

Any mode of attaining knowledge, distinct from Reasoning, 

is, of course, foreign from the present inquiry. 



LESSON XII. 



§ 1. The Dictum [or Maxim] above explained as the Uni- 
versal-principle of Reasoning,- will apply to a Syllogism^in 
8Dch a form as that of the examples given. ' Every (or No) 



Lesson xii.] terms of the conclusion. 91 

X is Y* ; Z (whether some Z or every Z) is X ; therefore 
■ — some, or every — Z is Y ; ' or ' No Z is Y ; ' or ' Some Z 
is not Y ; ' as the case may be. 

And in that form every valid argument may be exhibited. 

But there are other Syllogisms in other forms, to which 
the ' Dictum ' cannot be immediately applied, (though they 
may be reduced into the above form) and which yet are real 
Syllogisms, inasmuch as their conclusiveness is manifest from 
the form of expression, independently of the meaning of the 
Terms. 

For instance, ^ no Savages have the use of metals ; the an- 
cient Germans had the use of metals ; therefore they were 
not savages,' is a valid Syllogism, though the Dictum cannot be 
applied to it as here stated. But it may readily be reduced 
into the form to which the Dictum does apply ; by illatively- 
converting the Major-premise, into ' men who have the use of 
metals are not Savages.' 

But the argument as it originally stood was a regular Syl- 
logism ; and so are some others also in a different form ; 
although the Dictum does not immediately apply to them. 

Accordingly, certain rules [or ' Canons '] have been framed, 
which do apply directly to all categorical Syllogisms, whether 
they are or are not in that form to which the Dictum is im- 
mediately applicable. 

1st Canon. Two Terms which agree with one and the same 
third, may be pronounced to agree with each other : and 

2d Canon. Two terms whereof one agrees and the other 
disagrees with one and the same third, may be pronounced to 
disagree with each other. 

The technical sense of the words ' agree ' and ' disagree * 
have been explained in a former Lesson. 

The two Terms which are each compared with the same 



* See Lesson ix. \ 7. 



92 COMPENDIUM. [Part ii. 

third, are the Terms [or ' Extremes '] of the Conclusion ; viz. : 
the Major-term and Minor-term : and that third Term with 
which thej are separately compared in the two Premises, is 
the Middle-term. 

On the former of these two Canons rests the proof of af- 
firmative-conclusions ; on the latter, of negative. 

§ 2. To take first a Syllogism in the form originally given : 

* Every X is Y ; Z is X ; therefore Z is Y : ' or again * No 
X is Y ; Z is X ; therefore Z is not Y : ' in these examples, 

* Y ' and ' Z ' are in the two Premises respectively, compared 
with * X : ' in the former example they are assumed to * agree * 
with it ; and thence in the Conclusion, they are pronounced 
(according to the 1st Canon) to ' agree ' with each other ; in 
the latter example, * Y ' is assumed to ' disagree ' with ' X ' 
and ' Z,' to ' agree ' with it ; whence in the Conclusion they 
are pronounced (according to the 2nd Canon) to ' disagree * 
with each other. 

Again, to take a Syllogism in the other form, such as that 
in this Lesson, * No Savages &c.,' or, ' No Y is X ; Z is X ; 
therefore Z is not Y ; ' you will perceive that the 2nd Canon 
will apply equally well to this as to the preceding example. 

You will also find, on examination of the apparent-syllo- 
gisms [fallacies] — of which examples were given in former 
Lessons, and whose faultiness was there explained, — that 
they transgress against the above ^ Canons.' 

Take for instance, ' Some X is Y ; Z is X ; therefore Z is 
Y* ; ' and again * Every Y is X ; Z is X ; therefore Z is Y ; ' 
or ' every tree is a vegetable ; grass is a vegetable ; therefore 
grass is a tree : ' in these (as was formerly explained) the 
Middle-term is undistributed; [taken particularly in both 
premises] the two ' Extremes ' therefore [Terms of the Con- 
clusion] have been compared each with part only of the 

* See the example from Hume, respecting Testimony 



Lesson Xll.] TERMS OF THE CONCLUSION. 93 

Middle ; and thence we cannot say that they have each been 
compared with one and the same third: so that we are not 
authorized to pronounce their agreement or disagreement with 
each other. 

But remember, that it is sufficient if the Middle-term be 
distributed in one of the Premises ; since if one of the ' Ex- 
tremes ' (of the Conclusion) has been compared with part of 
the ' Middle ' and the other, with the tvhole of it, they have 
both been compared with the same ; since the whole must 
include every part. And accordingly, in the form originally 
given * Every X is Y ; Z is X ' &c. you may observe that the 
Middle-term is distributed in the Major-premise, and undis- 
tributed in the Minor. 

§ 3. Again, take the example formerly given, of ' illicit- 
process ; ' [proceeding from a term undistributed in the Pre- 
mise, to the same, distributed, in the Conclusion] as, ' Every 
X is Y ; Z is not X ; therefore Z is not Y ; ' or, ' Every tree 
is a vegetable ; grass is not a tree, therefore, grass is not a 
vegetable ; ' here the * Extremes,' which in the Conclusion 
are compared together, are not really what had been com- 
pared, each, with the Middle. For in the Conclusion, it is 
the whole of the term ' vegetable ' that is compared with the 
term ' grass ; ' (since negatives distribute the Predicate) though 
it was only part of that term that had been, in the Premise, 
compared with * tree ; ' the Predicate of an ' Affirmative * 
being undistributed. 

In tKis instance, therefore, as in the former one, the Canons 
have not been complied with ; each of these apparent-syllo- 
gisms having in reality four terms. 

You will observe, also, that when the Middle-term is am- 
higuous, there are, in sense, two Middle-terms, though you 
may have, apparently, a correct Syllogism : as ' Light is op- 
posite to darkness ; feathers are light ; therefore feathers are 
opposite to darkness.' The word ' light ' is here used equivo- 



94 COMPENDIUM. [^Part II. 

colly. (See the explanation in Lesson VII. § 3 of ^univocal* 
and ' equivocal.') 

So glaring an equivocation as this, could, of course, deceive 
rio one, and could only be employed in jest.* But when there 
is a very small difference between the two senses in which 
a Middle-term is used in the two Premises, then, though the 
reasoning is not the less destroyed, the equivocation is the 
more likely to escape notice. And men are practically de- 
ceived in this manner, every day, both by others, and by 
themselves. 

§ 4. For instance, there is an argument of Hume's (in the 
Work referred to in a former example, and which is said to 
have been convincing to some persons) which may be regu- 
larly stated, thus: ^Nothing that is contrary to experience 
can be established by testimony ; every miracle is contrary to 
experience ; therefore no miracle can be established by testi- 
mony.' Now the middle-term, ' contrary to experience,' ad- 
mits of being understood in either of two senses ; sometimes 
(and this is the strict and proper sense) it means ' what we 
know by our own experience to be false ; as, for instance, if 
several witnesses should depose to some act having been done, 
at a certain time and place, by a person known to me, and in 
whose company I was, at that time, and in a different place, 
I should be enabled to contradict their testimony from my 
own experience. 

Sometimes, again, the expression is^ employed to denote 
* something which we have never experienced, and have not 
known to be experienced by others : ' which would be the 
case with the ascent of a balloon, for instance, to one who had 
never seen or heard of such a thing ; or with the freezing of 
water, to a king of Bantam, mentioned by Hume. 



* Most jests, it is to be observed, — such as puns, conundrums, &c. — 
are mockjallacies. 



Lesson xii.] ambiguous middle-term. 95 

Now if the Term ' contrary to experience ' be understood 
in this latter sense in both Premises, then the Jlfo/'or-Premise 
of the Syllogism will be manifestly false ; since it would im- 
ply that the king of Bantam, or any one living in a hot 
Country, could have no sufficient reason for believing in the 
existence of ice. And if the term be understood (in both 
premises) in the other sense, then the Mi7ior will be false ; 
since a Man cannot say that he knows by his own experience 
(whatever he mav &e^^e^;e or judge, and however rightly) the 
falsity of every individual narrative of every alleged miracle. 

But if the term is in each Premise to be so understood as 
that each shall be true, then it is evident that it must be taken 
as two different terms, (in sense, though not in sound) no less 
than the term ' light ' in the former example. 

§ 0. As for the truth or falsity of any Premise, or the sense 
in which any Term is to be undertsood, in this or that Propo- 
sition, of course no fixed rules can be given ; as this must 
evidently be determined, in each case, by the subject-matter 
we are engaged on. 

But though no rules can be given for detecting and ex- 
plaining every fallacious ambiguity, it is useful to learn and 
to keep in mind where to seek for it : namely, to look to the 
Middle-term, (the argument having been first stated in a syllo- 
gistic form) and to observe whether that is employed precisely 
in the same sense in each Premise. 

As for the Terms of the Conclusion, there is not much 
danger of error or fallacy from any possible ambiguity in one 
of these ; since in whatever sense either of these is employed 
in the Premise, it will naturally be understood in the Conclu- 
sion, in that same sense ; though in itself it might admit of 
other meanings. 

If, for instance, any one should conclude that the ' Plantain ' 
is ' worth cultivation in places where it will flourish, because 
it produces a vast amount of human food,' you would under- 



1)6 COMPENDIUM. [Part II. 

stand him to mean, both in the Premise and the Conclusion, 
the fruit-bearing ' Plantain ' of the West Indies, and not the 
herb that grows in our fields. 

Sometimes, however, in a long train of Reasoning, a person 
may be led into error, by remembering merely that a certain 
Proposition has been proved, while he forgets in what sense it 
was proved. 

§ 6. There are six rules commonly laid down, as resulting 
from the two Canons above mentioned ; by which rules any 
apparent Syllogism is to be tested : since none can be objected 
to which does not violate any of these rules ; and any appar- 
ent-syllogism which does violate any of them, is not, in reality, 
conformable to the above Canons. 

i. A Syllogism must have three, and only three. Terms. 

ii. It must have three, and but three Propositions. 

iii. The Middle-term must be one only, [i. e. not doubW] 
and, therefore, must be unequivocal, and must be (in one at 
least of the Premises) distributed. 

iv. No Term is to be distributed in the Conclusion that was 
not distributed in the Premise : [or, there must be no ' illicit- 
process.'] 

V. One at least of the Premises must be affirmative ; since, 
if both were negative, the Middle-term would not have been 
pronounced either to agree with each of the '■ Extremes,' or to 
agree with one and disagree with the other ; but to disagree 
with both ; ' whence nothing can be inferred : as ' No X is Y ; 
and Z is not X,' evidently affords no grounds for comparing Y 
and Z together. 

And vi. If one Premise be negative, the Conclusion must 
be negative ; since — inasmuch as the other Premise must be 
affirmative — the Middle will have been assumed to agree 
with one of the * Extremes,' and to disagree with the other. 

All these rules will have been sufficiently explained in what 
has been already said. 



Lesson xii.] terms of a syllogism. 97 

And from these you will perceive that in every Syllogism 
one Premise at least must be Universal ; since, if both were 
Particular, there would be either an undistributed IVIiddle., or 
an Illicit-process. 

For if each Premise were I (Particular-affirmative) there 
would be no distribution of any Term at all ; and if the 
Premises were I and O, there would be but one Term, — the 
Predicate of O [the particular-negative] — distributed ; and 
supposing that one to be the Middle, then the Conclusion 
(being of course negative, by rule vi.) would have its Predi- 
cate — the Major-term — distributed, which had not been 
distributed in the Premise. Thus ' Some X is Y ; some Z is 
not X,' or again * Some X is not Y ; some Z is X,' would 
prove nothing. 

And for the like reasons, if one of the Premises be Particu- 
lar, you can only infer a Particular Conclusion : as * Every 
X is Y ; some Z is X,' will only authorize you to conclude 
* Some Z is Y ; ' since to infer a Universal would be an ' illicit- 
process of the Minor-term^ 

§ 7. What is called the ' Mood' [or ' Mode '] of a Syllo- 
gism, is the designation of the three Propositions it contains 
(in the order in which they stand) according to their respect- 
ive Quantity and Quality ; that is, according as each Propo- 
sition is A, E, I, or O. 

Looking merely at the arithmetical calculation of 'permuta- 
tions, (as it is called) all the possible combinations of the four 
Symbols, by threes, would amount to 64. For each of the 4 
admits of being combined, vn -pairs, with each of the 4; [as A, 
with A, with E, with I, and with O, &c.) which gives 16 pairs ; 
and each of these 1 6 pairs admits of being combined with each 
of the 4 as a third ; which gives 16X4 = 64. 

But it is plain that several of these combinations are such 
as oould not take place in a Syllogism. For instance E, O, 
O, could not be a Mood of any Syllogism, since it would have 
9 



98 COMPENDIUM. [^Part II. 

negative-premises (see Rule V.) nor I, O, ,0, which would 
have both premises particular, nor I, E, O, which would have 
aa illicit-process of the Major-term ; since the Conclusion, 
being negative, would have the Major-term distributed, while 
the Major-premise, being I, would have no term distributed. 
And so with many others. 

There will be found on examination to be in all only eleven 
Moods in which any Syllogism can be expressed : and these 
are. A, A, A, — E, A, E, — A, I, I, — E, I, O, — A, E, E, 

— A, O, O, — A, A, I, — I, A, I, — E, A, O, — O, A, O, 

— A,E, O. 

§ 8. What is called the ' Figure ' of a Syllogism, is, the 
situation of the Middle-term, in the two Premises respectively, 
with relation to the two ' Extremes ' [or Terms] of the Con- 
clusion, — the Major and Minor-terms. 

It is evident that all the possible collocations of the Middle 
must be four : since it must be either the Subject of the Major- 
premise and the Predicate of the Minor ; or the Predicate of 
each ; or the Subject of each : or the Predicate of the Major 
and Subject of the Minor. 

On looking to the examples originally given, you will see 
that a Syllogism in that form [' Every X is Y ; Z is X ; 
therefore Z is Y '] has the Middle-term made the Subject of 
the Major-premise, and the Predicate of the Minor. 

This is called the First Figure ; and it is to Syllogisms in 
this Figure alone that the ' Dictum ' above-mentioned will at 
ojice apply. 

§ 9. If you look to the forms afterwards exemplijQed, (§ 1 
of this Lesson,) as ' No savages, &c.' or ' No Y is X ; Z is X ; 
therefore Z is not Y,' you will see that the Middle is the 
Predicate of each Premise. This is called the Second Figure. 
And in this, evidently none but negative Conclusions can be 
proved ; since one of the Premises must be negative, in order 
tliat the ]\ildJle-tenn may be (by being the Predicate of a 
Negative) distributed. 



Lesson xii.] mood of a syllogism. 



99 



Again, the Middle-term may be the Subject of each Premise. 
And this is called the Third Figure. Thus ' Some X is Y ; 
every X is Z ; therefore some Z is Y ; ' is a correct Syllo- 
gism in the third Figure, being conformable to the first 
Canon. 

And the Syllogism here given as an example maybe easily 
reduced to the first Figure, by simply-converting the Major- 
premise, and taking it for the Minor; [transposing the 
Premises] which will enable you to infer the simple-converse 
of the. Conclusion : as ' Every X is Z ; Some Y is X ; there- 
fore Some Y is Z : ' and this implies that ' Some Z is Y ; ' 
since (as was explained formerly) the simple conversion of I 
is illative. 

For instance, 'some painful things are salutary; every 
thing painful is an object of dread ; therefore some things 
which are objects of dread are salutary ; ' this, though a valid 
Syllogism as it stands, may be reduced, in the manner above 
stated, to the first Figure. 

In this, or in other ways, any Syllogism in the third Figure 
maybe easily ' reduced' (as the technical phrase is) to the first 
Figure. 

In this third Figure you will find that none but Particular 
Conclusions can be drawn. To infer a Universal would 
always, you will find, involve an ' illicit-process of the Minor- 
term.' For if the Premises are both Universal, which (as we 
have already seen, (§ 6) they must always be, to warrant a 
Universal Conclusion) then, supposing them to be A, A, there 
will have been, — in this third Figure — no term distributed 
except the Middle ; (affirmatives not distributing the Predi- 
cate) and consequently no term can be distributed in the 
Conclusion ; which must, therefore, be I. 

And if the Premises be E and A, there will have l)cen 
(besides the Middle) only one term, — the Predicate of E, 
distributed; and consequently only one term can be dis- 



100 COMPENDIUM. \^Part II. 

tributed in the Conclusion ; and that one must be the Predi- 
cate of O ; since the Universal [E] would have both terms 
distributed. 

§ 10. The third Figure might be called the ^exceptive' or 
the 'refutatory' Figure; (or, agreeably to the expression 
of the Greek writers, the ' enstatic ; ') as being a very natu- 
ral form of expressing arguments which go to establish the 
contradictory of some Universal Proposition that any one may 
have maintained, or that may be generally believed. 

For instance, if any one were speaking of ' metals ' as being, 
universally, ' conductors of heat,' you might adduce ' Platina ' 
as an exception. Or should any one contend that ' no agent 
incapable of distinguishing moral good and evil (as, for in- 
stance, a madman) can be deterred from any act by appre- 
hension of punishment,' you might refute this, by adducing 
the case of a brute, — for instance, a dog — deterred from 
sheep-biting by fear of punishment. And such arguments 
would fall very naturally into the third Figure. 

It is, especially, the most natural form in which to express 
an argument — such as we often employ for the above pur- 
pose — in which the Middle-term is a Singular-term ; as when, 
for instance, you prove by the example of a certain individual,* 
the contradictory of a Proposition (which would seem to most 
persons a very probable conjecture) that a deaf and dumb 
person, born blind, cannot be taught language. 

The second Figure may be called the ' exclusive ' Figure ; 
being a very natural form for arguments used in any inquiry 
in which we go on excluding, one by one, certain suppositions, 
or certain classes of things, from that whose description we 
are seeking to ascertain. 

Thus, certain symptoms, suppose, exclude ^small-pox;' 
that is, prove this not to be the patient's disorder; other 



* See the Note on a former Lesson, on the case of Laura Bridgcnian. 



Lesson xiii.] figure of a syllogism. 101 

symptoms, suppose, exclude ' Scarlatina ' &c., and so one 
may proceed by gradually narrowing the range of possible 
suppositions. 

These three Figures are the only ones in which any argu- 
ment would, designedly, be stated. For, as to what is called 
the 4th Figure (in which the Middle-term is made the Pred- 
icate of the Major-premise and the Subject of the Minor) 
though a Syllogism so stated would be undeniably valid if 
conformable to the iniles (as ' every Y is X ; no X is Z ; 
therefore no Z is Y') this form is only a clumsy and inverted 
way of stating what would naturally be expressed in the 1st 
Figure ; as, in this example, might be done by transposing 
the Premises, and simply-converting the Conclusion. 



LESSON xni. 



§ 1. Besides (7«^e^onca^arguments, which we have been 
treating of. Reasoning is often expressed in a Hypothetical 
form. And though such arguments may be reduced into a 
categorical form, this is not necessary, except for the purpose 
of pointing out the sameness, in all cases, of the Reasoning- 
process. For you may exhibit in a hypothetical form, a per- 
fect ' Syllogism ' as above defined. 

A Hypothetical (or as some writers call it, a ' compound ') 
Proposition, consists of ' two or more Categorical-propositions, 
united by a Conjunction, in such a manner as to make them 
one proposition.' And the different kinds of hypothetical- 
proposition are named after their respective Conjunctions; 
9* 



1'02 COMPENDIUM. \_Part II. 

namely ' Conditional ' and ' Disjunctive*.' For instance, ' if 
A is B, then X is Y ' is a Conditional-propositionf ; ' either 
A is B, or X is Y ' is Disjunctive. 

And each of these is a real Proposition, i. e., asserts some- 
thing ; and consequently is either true, or false ; which (as 
was formerly explained) is peculiar to Propositions: and 
each is also one Proposition, though consisting of several 
parts [or ' members '] each of which, if taken separately, 
would be itself a Proposition ; but the Conjunction (which is 
called a Copula) makes the whole one Proposition. 

§ 2. For instance, ' the world is eternal,' is a proposition : 
' records earlier than the Mosaic exist,' is another proposition ; 
and ' z/the world be eternal, records earlier than the Mosaic 
must exist,' is a third proposition distinct from each of the 
other, and which may be true, though they be both false : 
since it does not assert the truth of either of them, but only 
the connexion between them. Again, should any one say ' if 
the Northern-lights be shining, some great revolution of an 
Empire is going on,' this would be, properly speaking, a false 
Proposition, even should it turn out that each of the ' mem- 
bers ' stated as a categorical-proposition, is true ; supposing it 
admitted that they have no connexion with each other. 

Observe, however, that no false Conclusion can be de- 
duced from a false Conditional-proposition, when it so happens 
that both its ' members ' (stated as categorical-propositions) 

are true. 

In the case of a Disjunctive-proposition on the other hand, 
it Is implied that one at least, of its ' members' (stated as a 
categorical-proposition) must be true, and that, if not, the 
whole Proposition must be false. As ' this man was either at 



* See Lesson X. 

t Those writers who use the word compound proposition instead of hj 
potheficd, employ ' hypothetical ' to signify ' conditional.' 



Lesson xiii.] hypothetical-propositions. 103 

Oxford or at Cambridge ' would not be true, if he were not at 
Oxford, and not at Cambridge. 

And it is usually meant to be understood that 07ily one of 
the members can be true : for if this were not the meaning in 
such an example as the foregoing, it would have been more 
correct to say ' this man was either at Oxford, or Cambridge, 
or hothJ 

§ 3. A l^y^o\he,i\Q,2X-syllogism is one in which the reasoning 
itself turns on the hypothesis ; not, every syllogism that has 
in it a. hypothetical premise ; for the ' hypothesis' may be a 
portion of one of the Terms, and the syllogism may be merely 
categorical. 

For instance, * Real miracles are evidence of a divine com- 
mission ; if the works of Jesus were acknowledged miraculous 
by the unbelieving Jews, they must have been real miracles ; 
therefore, the works of Jesus (if they were acknowledged, 
&c.) are evidence of a divine commission ; ' is a categorical 
syllogism; the hypothesis being merely a portion of the 
Minor-term. 

And so also with such an example as ' Every X is either 
Y or W ; Z is X ; therefore Z is either Y or W.' 

In a hypothetical-syllogism, properly so called, — that is, in 
which the reasoning is based on a hypothetical-premise, that 
premise is called the Major, and the other — which is cate- 
gorical — is called the Minor-premise. 

We will speak first of Oonditional-syWogi^ui^. 

There are in a Conditional-proposition two members, [cate- 
gorical-propositions] whereof one is asserted to depend on the 
other. That on which the other depends is called the ^Ante- 
cedent ; that which depends on it, the Consequent ; ' and the 
connexion between the two, (expressed by ' if,' or ' supposing') 
is called the ' consequence.^ 

(Consequence) (Antecedent) 

For instance 'If this man is a murderer > 



104 COMPENDIUM. \_Part II. 



(Consequent) (Consequent) 

he deserves death.' ' The Eno-Hsh are well off- 



(Consequence) (Antecedent) 

if they know their own advantages. 

The natural order is to place the ' Antecedent ' ^r5^ ; 
but this (as you will see from the example above) is not 
essential. 

§ 4. The meaning, then, of a Conditional-proposition, is, 
that ' the Antecedent being assumed to be t7-ue, the Consequent 
is to be granted as true also.' And this may be considered in 
two points of view : 1st, allowing that the Antecedent is true, 
the Consequent must be true ; 2ndly, supposing the Antece- 
dent were true, the Consequent would be true. 

Hence, there are two kinds of Conditional-syllogism ; 1st, 
if the Antecedent be (in the minor-premise) granted to be 
true, the Consequent may Cin the Conclusion) be inferred : 
2ndly, if the Consequent be not true — that is, if its Contra- 
dictory be assumed in the minor-premise — the Antecedent 
cannot be true ; that is, its Contradictory may, in the Conclu- 
sion, be inferred : since if the Antecedent hod been true, the 
Consequent (which we have assumed to be false) would have 
been true also. 

A Syllogism of the former kind, is called ' Constructive ; ' 
of the latter kind, ' Destructive.^ 

For instance, ' if A is B, X is Y : ' let this be the major- 
premise ; then if you add, ' but A is B ; therefore X is Y,' 
this forms a Constructive-syllogism : if you say ' X is not Y ; 
therefore A is not B,' this is a Destructive-syllogism. Thus, 
* if this river has tides, the sea into which it flows must have 
tides ; ' then if I add ' this river has tides,' it follows in Con- 
clusion, that ' the sea into which it flows has tides ; ' which 
is a Constructive-syllogism. If I add, ' the sea into which it 
flows has not tides,' it follows that ' this river has not tides.' 

§ 5. And here observe, by the way, that, in hypothetical- 
arguments, we are not concerned with the distinction between 



Lesson xiii.] conditional-proposition. lOo 

affirmative and negative Conclusions. For, of the two mem- 
bers of a Conditional-proposition, either, or both, may be 
affirmative, or may be negative ; so that we may estabhsh the 
truth ' constructively ' of either an affirmative or a negative 
Consequent ; or may (' destructively ') establish the falsity — 
that is, infer the Contradictory — of eif;her an affirmative or a 
negative Antecedent. 

For instance * if no miracles had been displayed by the first 
preachers of the Gospel, they could not have obtained a hear- 
ing ; but they did obtain a hearing ; therefore some miracles 
must have been displayed by them,' is a Destructive-condi- 
tional-Syllogism. 

The Consequent, as has been said, depends on the Ante- 
cedent ; so that, if the Antecedent be true, the Consequent 
will be true also ; but as the Antecedent does not depend on 
the Consequent, nothing is proved by denying the Antecedent, 
or again, by assuming the truth of the Consequent. Suppose 
it granted that 'if A is B, X is Y,' though it may indeed so 
happen that X is Y, only on that condition, — that is, that if 
X is Y, A is B, — this is not implied by the original asser- 
tion : so that (merely assuming that original assertion,) 
to add that * A is not B,' or again, to say * X is Y,' proves 
nothing. 

For instance, * if this man has committed theft he deserves 
punishment' does not authorize me to proceed either to say 
* he has not committed Iheft ; therefore he does not deserve 
pun.shment;' or again, ' he deserves punishment; therefore 
hs has committed theft.' For it is (in this case) evident that 
a man may deserve punishment for some other offence. 

§ 6. And you may observe, that the fallacy q^ affirming the 
Consequent and thence inferring the truth of the Antecedent, 
answers to the fallacy (in Categoricals) of undistributed mid- 
dle, or to that of negative-premises ; as may be seen from the 
above example. For to say ' every one who has committed 



106 COMPENDIUM. [^Part II. 

theft deserves punishment; and this man deserves punish- 
ment/ would evidently be a case of undistributed-middle. 
And again, if instead of saying ' if this man has a fever he is 
not fit to travel ; and he is not fit to travel ; therefore he has 
a fever,' you say ' no one who has a fever is fit to travel,' &c. 
there will be the fallaqjr of two negative-premises. 

The Fallacy again, of denying the Antecedent and thence 
inferring the denial of the Consequent, would correspond (in 
Categoricals) either to an 'Illicit-process of the Major-term,' 
or to the Fallacy of ' two negative-premises,' or that of intro- 
ducing palpably ' more than three terms.' For instance, sup- 
pose instead of saying ' if this man has committed theft &c.' 
you say, ' Every one who has committed theft deserves pun- 
ishment; this man has not committed theft, &c.' this would 
be an illicit-process of the Major. Or again, suppose, instead 
of saying ' if tliis man has a fever, he is not fit to travel ; but 
he has not a fever ; therefore he is fit to travel,' you say ' No 
one who has a fever is fit to travel ; this man has not a fever 
&c.' this would be to employ ' two negative-premises.' Again, 
' If this army is not brave it will not be victorious ; it is brave ; 
therefore it wiU be victorious ; ' would, if expressed categor- 
ically, have palpably more than three terms. 

§ 7. It is plain from what has been above said, that a Con- 
ditional-proposition may be illatively converted, by taking the 
Contradictory of the Consequent for an Antecedent, and (of 
course) the Contradictory of the Antecedent, for a Conse- 
quent. ' If A is B, X is Y ' implies that ' if X is not Y, 
A is not B.' ' If all wages be I'egulated by the price of food, 
an English laborer will have hio-her wao:es than an Ameri- 
can ; ' this manifestly implies, that, 'if an English laborer has 
not higher wages than an American, all wages are not regu- 
lated by the price of food.' 

This corresponds to the conversion of the categorical-i^ropo- 
sition A, 'by negation ;' [' contraposition,'] every Conditional- 



Lesson xiii.] conditional-proposition. 107 

proposition corresponding in fact to a Universal-alfirmative- 
Categorical : the A7itecedent answering to the Subject, and the 
Consequent, to the Predicate. 

It is evident, that if you thus convert the Major-premise 
[the hypothetical-premise] of any Condiliona.^ ^syllogism, you 
change the Syllogism from ' Constructive'' to Destructive^ 
or vice versa, from Destructive to Constructive. 

The Proposition ' if A is B, X is Y ' may be considered as 
amounting to this ; ' The case [or supposition] of A being B, 
is a case of X being Y.' And then to say (as in the Minor- 
premise and the conclusion, of a constructive-conditional syl- 
logism) ' A is B ; and therefore X is Y,' is equivalent to 
saying ' the present [or the existing] case is a case of A being 
B ; therefore this is a case of X being Y.' 

Or again, ' if the Stoics are right, pain is no evil ; but pain 
is an evil ; therefore the Stoics are not right,' (which is a 
destructive-conditional syllogism) may be reduced to a Cate- 
gorical, thus : ' To say that pain is no evil - - is not - - true ; 
to say that the Stoics are right - - is - - to say that pain is no 
evil ; therefore to say that the Stoics are right - - is not - - 
true.' 

This Syllogism is in the first Figure. The argument might 
be exhibited in the third Figure, thus : ' that pain is no evil is 
not true ; but that is maintained by the Stoics ; therefore some- 
thing maintained by the Stoics is not true.' 

In some such way (taking care always to preserve the 
same sense) any argument may be exhibited in various differ- 
ent forms of expression, (the choice of which is merely a 
matter of convenience) so as to point out and impress on the 
mind that the reasoning-process itself is always essentially one 
and the same, and may ultimately be referred to the ' Dic- 
tum ' formerly mentioned. 

§ 8. In a disjunctive-preposition, as has been already ob-- 
served, it is implied that at least some one of the ' members ' 



108 COMPENDIUM. [^Part II. 

must he true. If, therefore, all except one be (in the minor- 
premise) denied, the truth of the remaining one may be in- 
ferred. 

For instance, ' either the Gospel was an invention of im- 
postors, or it was a dream of fanatics, or a real revelation ; 
it was neither of the two former ; therefore it was a real rev- 
elation.' 

But if there be more than two members, and you deny (in 
the minor-premise) one or more of them, but not all except 
one, then you can only draw a disjunctive Conclusion ; as, 
' this event occurred either in Spring, Summer, Autumn, or 
Winter ; it did not occur in Summer or in Winter ; therefore 
it occurred either in Spring or in Autumn.' 

In a Disjunctive-proposition it is (as has been said above) 
usually understood that the members are exclusive ; i. e. that 
07ily one, of them can be true : and you may, on that supposi- 
tion, infer from the truth of one of them (assumed in the 
Minor) the Contradictory of the other, or others. As ' either 
A is B, or C is D, or X is Y ; but A is B ; therefore C is 
not D, nor is X Y.' 

§ 9. A Disjunctive-Syllogism may readily be reduced to a 
Conditional, by merely altering the form of the Major-pre- 
mise ; namely, by taking as an Antecedent the Contradictory 
of one or more of the members ; everything else remaining as 
before. Thus, in the example lately given, you might say, 
*i/^this did not occur in Summer nor in Winter, it must have 
occurred either in Spring or in Autumn ; ' &c. 

A Disjunctive-proposition, you are to observe, is, (as well 
as a Conditional) always affirmative. For, either kind 
of Hypothetical-proposition always affirms the connexion of 
the members of it [categorical-propositions contained in it] 
whether these be affirmative or negative propositions. 

And the contradiction of a Hypothetical-proposition must, 
therefore, consist in denying this connexion, ; which is done, 



Lesson XIV.] dilemma. 10^ 

not in a Hypothetical, but in a Categorical-propositioli. When 
it is asserted that ' if A is B, X is Y.' you would coLtradict 
this by saying ' it does not follow that if A is B, X must be 
Y ; * or by some such expression. Or when it is asserted 
that ' either A is B, or X is Y,' you might contradict this by 
saying ' it is possible that neither A is B, nor X, Y ; ' or you 
might contradict a Disjunctive-proposition by two or more 
Categorical propositions; namely, by asserting separately the 
Contradictory of each member ; as ' either some Z is Y, or 
else some W is not X,' might be contradicted by ' no Z is Y, 
and every W is X.' 



LESSON XIV. 



§ 1. It will often happen that you will have occasion to 
employ that complex kind of Conditional-syllogism (consisting 
of two or more such syllogisms combined^ which is commonly 
called a ' Dilemma.^ 

When you have before you as admitted truths two (or more) 
Conditional-propositions, with different Antecedents, but each 
with the same Consequent, and these Antecedents are such 
that you cannot be sure of the truth of any one of them, sepa- 
rately, but are sure that one or other must be true, you will 
then, naturally be led to state both of the Conditional-proposi- 
tions, first ; and next, to assert disjunctively the Antecedents ; 
and thus to infer the common Consequent. As ' if every A is 
B, X is Y ; and if some A is not B, X is Y ; but either every 
A is B, or some A is not B ; therefore X is Y.' 

This kind of Argument was urged by the opponents of Don 
Carlos, the pretender to tlie Spanish Throne ; which he 
10 



110 COMPENDIUM. \_Part TI. 

claimed as heir-male, against his niece the queen, by virtue 
of the Salic-law excluding females ; which was established 
(contrary to the ancient Spanish usage) by a former king of 
Spain, and was repealed by kmg Ferdinand. They say ' if a 
king of Spain has a right to alter the law of succession, Carlos 
has no claim : and if no king of Spain has that right, Cai'los 
has no claim ; but a king of Spain either has or has not, 
such right; therefore (on either supposition) Carlos has no 
3laim.' 

§ 2. "When several Conditional-propositions have different 
Consequents as well as different Antecedents, then we can 
only disjunctively infer those Consequents : that is, we can 
only infer that (supposing some one or other of the Antect 
dents true) one or other of the Consequents must be true. As, 
* if A is B, X is Y ; and if C is D, P is Q ; but either A is 
B, or C is D ; therefore either X is Y, or P is Q.' Thus, ' if 
the obedience due from Subjects to Rulers extends to reli- 
gious worship, the ancient Christians are to be censured for 
refusing to worship the heathen idols ; if the obedience, &c., 
does not so extend, no man ought to suffer civil penalties on 
account of his religion ; but the obedience, &c., either does 
60 extend, or it does not ; therefore either the ancient Chris- 
tians are to be censured, &c., or else no man ought to suffer 
civil penalties on account of his religion.' 

So also, ' if man is capable of rising, unassisted, from a sav- 
age to a civilized state, some instances may be produced of a 
race of Savages having thus civilized themselves ; and if Man 
is not capable of this, then, the first rudiments of civilization 
must have originally come from a super-human instructor ; 
but either Man is thus capable, or not ; therefore either sonie 
such instance can be produced, or the first rudiments, &c.' 

§ 3. And when there are several Antecedents each with a 
different Consequent, tlien, we may have a Destructive- 
dilemma : that is, we may, in the Minor-premise disjunct I ccly 



Lesson xiv.] dilemma. 1 1 1 

deny the Consequents, and in the Conclusion disjunctively 
deny the Antecedents. Or again, you may have a Dilemma 
partly Constructive and partly Destructive ; that is, in the 
Minor-premise (which in a Dilemma is always a Disjunctive- 
proposition) the members — suppose, for instance, there are 
two, — may be, one of them, the assertion of the Antecedent 
of one of the Conditional-propositions, and the other, the con- 
tradictory of the Consequent of the other Conditional. 

Suppose we say, 'if X is not Y, A is not B ; and if P is 
not Q, C is not D ; but either A is B, or C is D ; therefore 
either X is Y, or P is Q ; ' this would be a Destructive-Di- 
lemma ; and you may see that it corresponds exactly with the 
example given a little above, only that we have, here, con- 
verted both of the Conditional-propositions. See § 7 of the 
preceding Lesson. If w^e had converted one only, and not, the 
other, of the Conditionals, (as ' if A is B, X is Y ; and if P is 
not Q, C is not D ; ' &c.,) then the Dilemma w^ould have been 
partly Constructive and partly Destructive. For, as has been 
formerly explained, the Difference between a Constructive 
and a Destructive Syllogism consists merely in the form of 
expression, and it is very easy to reduce either form into the 
other. 

It may be worth while to observe, that it is very common 
to state the i)!f^?^or-premise of a Dilemma first ; in order to 
show the more clearly that the several Categorical proposi- 
tions which are, each, doubtful, w^hen taken separately, may 
be combined into a Disjunctive-proposition that admits of no 
doubt. And this Minor-premise being disjunctive, some have 
hence been led to suppose that a Dilemma is a kind of dis- 
junctive argument ; tliough it is really, as we have shown, a 
Conditional. 

The name of ' Z)?"Iemma., again, has led some to suppose, 
that it must consist o^ two members only; though it is evident 
that there may be any number. 



112 



COMPENDIUM. \_Fart II. 



§ 4 When there is a long series of arguments, the Conclu- 
sion of each being made one of the Premises of the next till 
you arrive at your ultimate Conclusion, it is of course a tedious 
process to exhibit the whole in the form of a series of Syllo- 
gisms. This process may in many cases be considerably 
abridged, without departing from the strict syllogistic-form: 
rthat is, such a form as shows the conclusiveness of the rea- 
sonino-, from the expression alone, independently of the mean- 
ing of the Terms, and equally well when arbitrary Symbols 
are used to stand for the Terms.] , . .. . 

What is called a ' Sorites ' (from a Greek word signifying 
a heap, or pile) is such an abridged form of stating a train of 
arguments. When you state a series of propositions m which 
the Predicate of the first is made the Subject (distributed) of 
the next, and the Predicate of that, again, in like manner, the 
Subiect of the next, and so on, to any length, you may then 
predicate in the Conclusion the Predicate of the last Premise 
of the Subject of the first. ^ 

Thus ^ A (either" some" or "every") is B; every B is 
C • every C is D ; every D is E ; &c. therefore A is E ; ' or 
^ no D is E ; therefore A is not E.' Thus, also, ' this man is 
selfish ; whoever is selfish is neglectful of the good of others ; 
whoever is neglectful of the good of others is destitute of 
friends; and whoever is destitute of friends is wretched; 
therefore this man is wretched.' 

§ 5 To such a form of argumentation the ' Dictum tor- 
merly treated of may be applied, with one small addition, 
which is self evident. ' Whatever is afiirmed or denied of a 
whole Class, may be affirmed or denied of whatever is com- 
prehended in lariy Class that is wholly comprehended «n] that 
Class ' This sentence, omitting the portion enclosed in brack- 
ets you will recognize as the ' Dictum,' originally laid down : 
and the words in brackets supply that extension of it which 
tnakes it applicable to a ' Sorites,' of whatever length; smce 



Lesson xiiv.] sorites. , 118 

it is manifest that that clause might be enlarged, as far as you 
will, into ' a Class that is wholly comprehended in a Class, 
which again is wholly comprehended in another Class, &c.' 

You will perceive, on looking at the above examples, that, 
though the first of the propositions of a Sorites may be either 
Universal or Particular, all the succeeding Premises must be 
Universal; since, else, the ' Dictum,' as stated just above, 
would not apply. 

You will perceive also that, though the last of the Premises 
may be either Negative or Affirmative, all the preceding ones 
must be Affirmative, in order that the Dictum may be appli- 
cable. Thus, in the example, first given, it is allowable to 
say ' no D is E ; therefore A is not E ; * but then it is neces- 
sary that ' C ' should be comprehended in ' D ' (not excluded 
from it) and ' B ' likewise in ' C,' and ' A ' in ' B,' since other- 
wise the ' Dictum ' would not be applicable. 

§ 6. It will be seen, on examining the examples, that there 
are, in a Sorites, as many Middle-terms as there are interme- 
diate propositions between the first and the last ; and that it 
may be stated in just so many separate syllogisms in the 1st 
Figure ; which is the simplest and most common form of a 
syllogism. 

The first of these syllogisms will have for its J/oyor-pre- 
mise the second of the propositions in the series, and for its 
Jt^'wor-premise, the first of them : and the Conclusion of this 
first syllogism will be a proposition which is (in the Sorites) 
not expressed but understood ; and which will be the Minor- 
premise of the next Syllogism. And of this next syllogism 
the Major-premise will be the third that is expressed in the 
Sorites ; and so on. 

For instance, (1st,) ' every B is C ; A is B ; [therefore A 
is C;'] and (2dly) 'every C is D;' [' A is C ; therefore A 
is D,'] &c. 

10* 



114 



COMPENDIUM. \_Pa7^ II. 



The portions, enclosed in brackets are those which in the 
Sorites are understood. 

The only Minor-^vemise expressed in the Sorites is the first 
proposition of the Series; all the succeeding minor-premises 
being understood. 

And hence it is that (as has been above said) this fii'st is 
the only one of all the Premises that may allowably be a 
Particular: because, in the first Figure, though the Minor 
may be either Universal or Particular, the Major (as you see 
from what was formerly said, of the ' Dictum,') must always 
be Universal; and aU the premises in the Sorites except the 
first, are Jfajor-premises. 

In this way may also be explained what was above said, 
that the last of the premises of a Sorites is the only one that 
can allowably be a Negative: since if any of the others were 
negative, the result would be that one of the Syllogisms of 
the Series would have a negative minor-premise ; which, m tbe 
first Figure (as you will see by again referring to the ' Dic- 
tum ') is inadmissible. 

§ 7. A series of Conditional-sjllogisms (which correspond, 
as has been shown, to Categorical-syllogisms in the first 
Fi-ure) may i^ like manner be abridged into a Sorites ; by 
mrkin- the Consequent of the first proposition the Antecedent 
of the next ; and so on : and then drawing the Conclusion by 
either asserting the frst Antecedent, and thence (construc- 
tively) inferring the last Consequent, or else, denpng the 
to of the Consequents, and (destructively) inferring the 
CDntradictory of tlie first Antecedent. ' As, ' K A is B, C is 
D ; and if C is D, E is F ; and if E is F, G is H,' &c. : and 
then, if the Sorites be ' Constructive,' you add ' but A is B ; 
therefore G is H ; ' or, if 'destructive,' 'but G is not H; 
therefore A is not B.' 

The foregoing are all the forms in which Reasomng can be 



Lesson xiv.] enthymeme. 115 

exhibited Syllogistically ; i. e. so that its validity shall be man- 
ifest from the mere form of expression. 

For, an Enthymeme, (see Lesson II. § 3) is manifestly not 
syllogistic ; since it is possible to admit the truth of the one 
premise that it is expressed, and yet to deny the Conclusion. 

An Enthymeme may indeed be such (since it contains all 
the three Terms requisite for a Syllogism,) that we can read- 
ily perceive what the premise is that ought to be understood, 
and which if supplied, would make the Syllogism complete : 
as ' Z is X ; therefore Z is Y ; ' [or ' the Elk has horns on the 
head ; therefore it is a ruminant '] this would be syllogistic, 
if you were to prefix ' Every X is Y ; ' but whether this be 
the Premise actually meant to be understood, we can only 
judge from the sense of the words that are expressed, and from 
what we believe respecting the subject-matter in hand, and 
the design of the Speaker. 

In a Syllogistic form, on the other hand, — whether Cat- 
egorical, or Hypothetical, and whether at full length, or 
abridged into a Sorites — that which is actually expressed in 
the Premises is such that no one can possibly suppose these 
true (whatever be the meaning of the Terms, or whether we 
understand them or not) without admitting the truth of the 
Conclusion thence drawn. 

§ 8. As for any arguments that are not expressed in a 
regular form, of course no precise rules can be laid down for 
reducing them into such a form ; since any arguments to 
which such rules do apply, must evidently be, on that very 
ground, pronounced to be already syllogistic. Some general 
remarks, however, (drawn chiefly from what has been taught 
in the foregoing Lessons) may be practically serviceable in 
he operation of reducing arguments into regular form. 

i. It has been remarked (in Lesson HI. § 7) that men are 
very impatient of tedious prolixity in Reasoning; and tliat 
the utmost brevity, — the most compressed statement of argu- 



116 COMPENDIUM. [^Part II. 

mentation, — that is compatible with clearness, is always 
aimed at, and is, indeed, conducive to clearness. And hence 
(as was pointed out) a single sentence, — or even a word, — 
will often be a sufficient hint of an entire syllogism. 

And it may be added, that such a sentence will sometimes 
be in the form, not of a Proposition, but of an Exclamation, 
— a Question, or a Command; and yet will be such as read- 
ily to suggest to the mind a Proposition. 

For instance, in some of the examples lately given, one 
might say (in place of one of the Propositions) ' Choose which 
you will of these two suppositions ; ' or ' Who can doubt that 
so and so follows ? ' 

The message to Pilate from his wife* furnishes an instance 
of a single word Qjust ') suggesting a Major-premise, while 
the Conclusion is stated in the form of an exhortation : ' have 
thou nothing to do with that Just man.' And the succeeding 
sentence must have been designed to convey a hint of Argu- 
ments for the proof of each of the Premises on which that 
Conclusion rested. 

§ 9. ii. Remember that (as was formerly shown) we may 
change any proposition from Affirmative to Negative, or vice 
versa, without altering the sense : it being the same thing, for 
instance, to affirm of any one the term ' not happy,' or to 
deny ' happy.' So that an argument may be valid which might 
appear, at the first glance, to have ^ negative premises.' 

But if the above experiment be tried in an argument that 
is really faulty on that ground, the only effisct will be, to chan2;e 
one fallacy into another : as ' A covetous man is not happy ; 
this man is not covetous; therefore he is happy:' here, if 
you take ' happy ' as the predicate of the Major, you have 
negative-premises : if you take ' not happy ' [or ' unha})py '] 
us the term, you will have four terms. 

Miitt. 27, 19. 



Lesson XIV.] CONVERSION-BY-NEGATION. Hi 

On the other hand, ' no one is happy who is not content ; 
no covetous man is content ; therefore no covetous man is 
happy,' is a valid syllogism. 

That the Conversion-by-negation [contra-position] of a Uni- 
versal-affirmative, is illative, has been formerly explained. 
And it is very common, and often conducive to clearness, to 
state such a proposition (A) in the form of this its converse 
(E) ; as, for instance, instead of 'every motive that could 
have induced this man to act so and so, must have been purely 
benevolent,' to say ' no motive but pure benevolence could 
have induced him to act so.' 

iii. Remember that one single sentence (as was formerly 
explained, Lesson IX. § 7) may imply several distinct propo- 
sitions, according to the portions of it which you understand as 
the Subject, and as the Predicate. For instance, ' It is the duty 
of the Judge to decide for him who is in the right ; this plain- 
tiff is in the right ; therefore it is the Judge's duty to decide 
for him,' might be understood as having Jive terms : but ac- 
cording to the drift of the first premise (considered as a part 
of this argument) what you are speaking of is, not, ' the duty 
of the Judge,' but ' the person who is in the right ; ' of whom 
you assert that ' he is fairly entitled to the Judge's decision on 
his side.' And if thus stated, the argument will be seen to be 
valid. 

And here it may be remarked, that to state distinctly as 
Subject and Predicate, that which is really spoken of, and that 
which is said of it, will be often the best and most effectual 
exposure of a Fallacy ; which will always be the more likely 
to escape detection, the more oblique and involved is the ex- 
pression. 



PART III. 
SUPPLEMENT. 



LESSON XV. 



§ 1. There are some other teclmical-terms, which it is 
useful to be familiar with, and which we will therefore now 
proceed to treat of in a supplementary Lesson. They are such 
as are usually introduced in an earlier place, previously to the 
matter of the last five Lessons. But it has been thought 
better to postpone everything that was not indispensable for 
the right understanding of what has been said concerning the 
several forms of Syllogism. 

A ' Common-term,' we have seen, is so called from its 
expressing what is common to several things ; and is thence 
called also a ' Predicable,' inasmuch as it can be affirmatively- 
'predicated, in the same sense [' univocally '] of certain other 
terms. It is evident that the word ' Predicable ' is relative^ 
i. e. denotes the relatio7i in which some Term stands to some 
other, of which it can be predicated. And this relation is of 
different kinds : in other words, there are several Classes [or 
Heads] of Predicables. 

When you are asked concerning any individual thing, 
* what is it ? ' the answer you would give, if strictly correct^ 
would be what is technically called its ' Species : ' as ' this is 
a pen ; ' ' that is a man ; ' ' this is a circle ; ' ' that is a mag^ 
net^ &c. 

And the ' Species ' of anything is usually described in tech- 
nical language as expressing its * whole Essence ; ' meaning, 
the whole of what can be expressed by a Obmmow-term : for 



Lesson x^y.j difference. 119 

it is plain, that, (as was formerly shown) it is only by taking 
an inadequate view of an ' Individual,' so as to abstract from 
it what is common to it with certain other individuals, disre- 
garding all that distinguishes it from them (including its actual 
existence as a single object) — it is only then, I say, that we 
can obtain any Common-term. 

§ 2. When the same question ' what is this ? ' is asked re- 
specting a SpecieSyi\i^ term by which you answer, is, that 
Predicable which is technically called the ' Genus ' of that 
Species. As, * what is a ^ pen ? ' answer ' an Instrument ; ' [a 
hind, or species of Instrument] ' what is a circle ? ' ' a curvili- 
near-plane-figure : ' so also ' a magnet ' would be said to be ' a 
Species [or kind] of Iron-ore,' &c. 

When you are asked ' what kind of [or " what sort of "] 
instrument is a pen ? ' you would answer, one ' designed for 
writing ; ' this being what characterizes it, and distinguishes it 
from other instruments : ' what kind of animal is Man ? ' the 
answer would be ' rational ; ' as distinguishing the Species 
from other animals ; ' what kind of plane-curvilinear-figure is 
a circle ? ' answer, ' one whose circumference is everywhere 
equidistant from the Centre ; ' which circumstance distinguish- 
es it from an Ellipse : &c. 

Such a Predicable, then, is technically called the ' Differ- 
ence ; ' [or, by the Latin name, ' Differentia '] in popular 
language, frequently, the ' Characteristic,' or the ' distinguishing 
point.' And the ' Difference ' together with the ' Genus,' are 
technically spoken of as ' constituting ' [' making up '] the 

* Species.' 

Any quality [or ' attribute '] which invariaMy and pecu- 
liarly belongs to a certain Species, but which yet is not that 
which we fix on as characterizing the Species, is technicnlly 
called a 'Property ;^ [or 'Proprium'] of that Species. Thus, 

* risibility ' [or the faculty of laughter] is reckoned a ' Prop- 
erty ' of Man : one of the ' Properties ' of a Circle, is, that any 
imgle drawn in a semi-circle, is a i-ight-angle : &c. 



120 SUPPLEMENT. [P«r^ III. 

The power of ' attracting iron ' might be taken as the * dif- 
ference ' [or ' characteristic '] of a magnet ; and its ' Polar- 
ity ' as a ' Property : ' or again, this latter might be taken 
as its Difference, and the other, reckoned among its Prop- 
erties. 

For it is evidently a mere question of convenience, which, 
in any such case, we fix on as the Characteristic of the Species 
we are contemplating. And either the one arrangement, or 
the other, may be the more suitable, according to the kind of 
pursuit we may be engaged in. 

An Agriculturist, for instance, (see Lesson 8, § 5) would 
not characterize each kind of plants in the same way as a Bot- 
anist, or again, as a Florist : no more would a Builder, and a 
Geologist, and a Chemist, characterize in the same way the 
several kinds of stones. 

§ 3. Any Predicable which belongs to some (and not to 
other) individuals of the same Species, [or which 'may be 
present or absent, the Species remaining the same '] is called 
an ^ Accident^ 

And these are of two kinds. A ' Separable-accident ' is 
one which may be removed from the Individual ; ' [or, which 
may be absent or present, in that which we regard as one and 
the same individual] as, for instance (in an example formerly 
given) the ' Sun ' is regarded as the same individual thing, 
whether ' rising,' or ' setting,' or in any other situation rela- 
tively to the spot we are in : ' rising,' therefore, or ' setting,' 
are separable accidents of the Sun. 

So, also, to be in this or that dress, or posture, would be a 
separable accident of an individual man ; but to be a native 
of France, or of England, or to be of a certain character, 
would be an ' inseparable accident.' 

It is by inseparable-accidents that we commonly distinguish 
one Individual from another of the same species. And to 
enumerate such Accidents is called ' giving a Description.' 
rSee § 10.) 



Lesson xv.] division. 121 

Of course, it is only from individuals that any * Accident ' 
call be ' inseparable ; ' for anything that is inseparable from a 
Species, [or, which forms a part of the signification of a Term 
by which we denote a certain Species] is not an Accident, but a 
Property. 

§ 4. Some writers enumerate among Properties such Predi- 
cables as are peculiar but not universal ; that is, which do not 
apply, each, to every individual of a certain species, but are 
peculiar to that species : as Man alone can be ' virtuous,' — 
can be a ' philosopher,' &c. which are attributes not belonging 
to man. But these are more correctly reckoned Accidents ; 
though Accidents peculiar to the Species. 

Some again speak of ' Properties,' which are universal but 
not peculiar ; as • to breathe air ' belongs to the whole human 
species, but not to that species alone. Such a Predicable, 
however, is not, strictly speaking, a Property of the Species 

* Man,' but a Property of a higher [more comprehensive'] 
Species, ' land-animal ; ' which stands in the relation of ' Ge- 
nus ' to the species ' Man.' And it would be called, ac- 
cordingly, in the language of some writers, a * ^ewmc-prop- 
erty ' of Man. A Property, strictly so called, of any Species 
under our consideration, would be called its ' 5^ec(^c-property.' 

Predicables, then, have been usually divided into these 
five heads : ' Genus, Species, Difference, Property, and Ac- 
cident.' 

You are to remember, that, as every Predicable is so called 
in relation to the Terras of which it can be (affirmatively) 
predicated, so, each Common-term is to be regarded as belong- 
ing to this or that Head of Predicables, according to the Term 
to which it is, in each instance, applied, or which may be ap- 
plied to it. Thus, the term ' Iron-ore ' is a Species in respect 
of the term ' Mineral,' and a Genus in respect of the term 

* Magnet ; ' and so, in other instances. 

§ 0. When we ' enumerate distinctly ' [or ' separately '] 
11 



]22 SUPPLEMENT. \_Part III. 

the several things that are signified by one Common-term, — « 
as the several species included under some Genus — we are 
said to ' divide ' that Common-term. Thus, ' natural-produc- 
tions ' are divided into ' Animal, Vegetable, and Mineral ; ' 
and each of these again may be subdivided into several ' mem- 
bers ; ' and so on. 

Perhaps the word ' distinguish^ if it had been originally 
adopted, would have been preferable to ' divide : ' (which, 
however, has been so long in general use in this sense, that 
it could not now be changed) because ' Division ' being (in 
this sense) a metaphorical word, the 'Division ' we are now 
speaking of is liable to be confounded with 'Division' in 
the other (which is the original and proper) sense of the 
word. 

' Division,' in its primary sense, means separating from each 
other (either actually, or in enumeration) the parts of which 
some really-existing single object consists : as when you di- 
vide ' an animal ' (that is, any single animal) into its several 
members ; or again, into its ' bones, muscles, nerves, blood- 
vessels,' &c. And so, with any single Vegetable,' &c. 

Now each of the parts into which you thus ' physically ' 
(as it is called) divide ' an animal,' is strictly and properly 
a ' part,' and is really less than the whole ; for you could not 
say of a bone, for instance, or of a limb, that it is ' an Animal.' 

But when you ' divide ' — in the secondary sense of the 
word ' (or, as it is called, ' metaphysically ') — ' Animal,' that 
is the Genus 'Animal,' into Beast, Bird, Fish, Reptile, Insect, 
&c., each of the parts [or ' members '] is metaphorically called 
a ' part,' and is, in another sense, more than the whole [the 
Genus~\ that is thus divided. For you may say of a Beast Or 
Bird that it is an ' Animal ; ' and the term ' Beast ' implies 
not only the term ' Animal,' but something more besides ; 
namely, whatever ' Difference ' characterizes '■ Beast ' and sep- 
arates it from ' Bird,' ' Fish,' &c. 



Lesson xv.] division. 123 

And so also any Singular-term [denoting one individual] 
implies not only the whole of what is understood by the Spe- 
cies it belongs to, but also more ; namely, whatever distin- 
guishes that single object from others of the same Species : as 
' London ' impHes all that is denoted by the term ' City,' and 
also its distinct existence as an individual city. 

§ 6. The parts [' members '] in that figurative sense with 
which we are now occupied, are each of them less than th^ 
whole, in another sense ; that is, of less comprehensive significa- 
tion. Thus, the Singular-term ' Romulus ' embracing only 
an individual-king, is less extensive than the Species ' King ; ' 
and that, again, less extensive than the Genus * Magis- 
trate,' &c. 

An ' i/zdividual,' then, is so called from its being incapable 
of being (in this figurative sense) divided. 

And though the two senses of the word * Division ' are 
easily distinguishable when explained, it is so commonly 
employed in each sense, that through inattention, confusion 
often ensues. 

We speak as familiarly of the * division ' of Mankind into 
the several races of ' Europeans, Tartars, Hindoos, Negroes,' 
&c. as of the * division ' of the Earth into ' Europe, Asia, Afri- 
ca,' &c., though ' the Earth ' [or ' the World '] is a Singular- 
term, and denotes what we call one Individual. And it is 
plain we could not say of Europe, for instance, or of Asia, 
that it is * a World.' But we can predicate ' Man ' of every 
individual European, Hindoo, &c. 

And here observe that there is a common colloquial incor- 
rectness, (increasing the liability to confusion) in the use of 
the word ' division,' in each of these cases, to denote one of the 
^ parts ' into which the whole is divided. Thus, you will some- 
times hear a person speak of Europe as one ' division ' of the 
Earth ; or of such and such a ' division ' of an Army ; meaning 
^portion' And so, again, a person will sometimes speak of 



124 SUPPLEMENT. \^Part IT 

* animals that belong to the feline division of the Carnivora, 
[flesh-eating-animals] meaning, that portion of the class ' Car- 
nivora.' 

§ 7. Division, in the sense in "which we are here speaking 
of it, (the figurative) is evidently the reverse process to ' Gen- 
eralization/ (See Lesson VII. § 4.) For as, in general- 
izing, you proceed by laying aside the differences between 
several things, and abstracting that which is common to them, 
so as to denote them, — all and each, -— by one Common-term, 
so, in dividing, you proceed by adding on the differences, so as 
to distinguish each by a separate term. 

When you take any Common-term to be divided and sub- 
divided, for any purpose you have in hand, — as, the Term 
^ Animal ' in a work on Zoology, — that Term is called your 

* Summum [highest] genius' the several Species into which 
you proceed to divide it, a,nd which are afterwards divided 
each into other Species, are called, each of them, a * Subal- 
tern ' Species or Genus ; being, each, a Species in relation to 
that which can be predicated of it, and a Genus, in relation to 
the Species of which it can be predicated. 

Thus ^ Iron-ore ' (in the example lately given) is a Subal- 
tern Species, or Genus, in relation to ' Mineral ' and to ' Mag- 
net,' respectively. 

Any Species that is ' not made a Genus of any lower Spe- 
cies ' in the division you happen to be engaged in, — or, in 
other words, which is not regarded as any further divisible 
except into individuals, — is usually called (by the Latin 
name) ' infima Species ; ' that is, the ' lowest Species.' 

* Proximum Genus ' is a technical name often used to denote 
the ' Genus-next-above ' [or ' nearest,'] the Species you may 
be speaking of: as 'Iron-ore' would be the ^nearest' [proxi- 
mum] Genus, of IMagnet ; and ' Mineral ' would be its 7nore 
remote Genus; that is, the Genus of its Genus. 

§ 8. It is usual, when a long and complex course of Di- 



Lesson xv.] tree of division. 125 

vision is to be stated, to draw it out, for the sake of clearness 
and brevity, in a form like that of a genealogical 'Jree.' 
And, by carefully examining any specimen of such a * Tree/ 
(going over it repeatedly, and comparing each portion of it 
with the explanations above given) you will be able perfectly 
to fix in your mind the technical terms we have been ex- 
plaining. 

Take, for instance, as a ' Summum-genus,' the mathemati- 
cal-term 

' Plane-superficial-figure ' 

I "1 I 

Mixed Figure Rectilinear Figure Curvilinear Figure 
(of Rect. and Curv.) 



1 I I 

Triangle Quadrilateral, &c. Circle Ellipse, &c. 

Such a ' Tree of division ' the Student may easily fill up for 
himself. And the employment of such a form will be found 
exceedingly useful in obtaining clear views in any study you 
are engaged in. 

For instance, in the one we have been now occupied with, 
take for a Summum-Genus, * Expression ; ' (^. e. ' expression- 
in-language ' of any such mental-operation as those for- 
merly noticed) you may then exhibit, thus, the division and 
subdivision of — 



11% 



126 



TREE OF EXPRESSION. 



[^Part III. 






■11- 






o 



- o- 



tn O 5? 



O o 



-cog 

.tf'^ bb 









fcO 



Jo O 
PL, as 
2t3 






a% 



2 s 



e.S 



Ph. 



>; 
^ 






C3 03 S** 

^ . s 






:^ 



o 

-a 

o 
O 



PI 



Pl, O 



- © o 



Lesson xv.] rules for dividing. 127 

§ 9. The rules for dividing correctly, are, 

i. That the whole [or Genus-to-be-divided] be exactly 
equal to all the Parts [or Members] together. Nothing, 
therefore, must be included, of which the Genus can not 
be (affirmatively) predicated ; — nothing excluded^ of which 
it can. 

ii. The Members [Parts] must be ' contradistinguished,' 
(or, as some writers express it, ' opposed ') and not include 
one another ; which they will do if you mix up together tu o 
or more kinds of division, made by introducing several dis- 
tinct classes of differences. 

Thus, if you were to divide ' Books ' into ' Ancient, Mod- 
ern, Latin, French, English, Quarto, Octavo, Poems, Histo- 
ries,' &c., (whereof a * modern-book ' might be ' French,' or 

* English,' — a ' Poem,' or a ' History,' &c., a ' Quarto-book,' 

* ancient ' or ' modern,' &c.) you would be mixing together 
four different kinds of divisions of Books ; according to their 
Age, Language, Size, and Subject. 

And there are what are called Gross-divisions ; (because 
they run across each other, like vertical and horizontal sections 
of anything) being divisions formed according to ' distinct 
classes of Differences : ' or, in other words, ' on several distinct 
principles of Division.' 

It is a useful practical rule, whenever you find a discussion 
of any subject very perplexing, and seemingly confused, to 
examine whether some ' Cross-division ' has not crept in unob- 
served. For this is very apt to take place : (though, of course, 
such a glaring instance as that in the above example could not 
occur in practice) and there is no more fruitful source of in- 
distinctness and confusion of thought. 

When you have occasion to divide anything in several 
different ways, — that is, ' on several principles-of-division,' 
— you should take care to state distinctly how many divisions 
you are making, and on what principle each proceeds. 



128 SUPPLEMENT. [^Part III, 

For instance, in the ' Tree ' above given, it is stated, that 
' Propositions ' are divided in different ways, ' according to ' 
this and that, &c. And thus the perplexity of Cross-division 
is avoided. 

§ 10. iiily. A Division should not be ' arbitrary ; ' that is, 
its members should be distinguished from each other by ' Differ- 
ences ' (see above § 7) either expressed or readily understood ; 
instead of being set apart from each other at random, or with- 
out any sufficient ground. For instance, if any one should 
divide ' coins ' into ' gold-coins,' ' silver,' and ' copper,' the 
ground of this distinction would be intelligible ; but if he should, 
in proceeding to subdivide silver-coin, distinguish as two 
branches, on the one side, ' shillings,' and on the other ' all 
silver-coins except shillings,' this would be an arbitrary Di- 
vision. (See below, § 13.) 

ivly. A Division should be clearly arranged as to its Mem- 
bers ; that is, there should be as much subdivision as the oc- 
casion may require ; and not a mere catalogue of the ' lowest- 
Species,' omitting intermediate classes [' subaltern '] between 
these and the ' highest genus : ' nor again an intermixture of 
the ' subaltern,' and ' lowest-species,' so as to have, in any two 
branches of the division. Species contradistinguished and placed 
opposite, of which the one ought naturally to be placed higher 
up [nearer the ' Summum '] and the other lower down in the 
Tree. 

For instance, to divide ' plane-figure ' at once, into ' equi- 
lateral-triangles, squares, circles, ellipses,' &c., or again ' vege- 
table,' into ' Elms, pear-trees, turnips, mushrooms,' &c., or 
again to divide ' Animal ' into ' Birds, Fishes, Reptiles, Horses, 
Lions,' &c. would be a transgression of this rule. 

And observe that, (as was foi'merly remarked) although 
such glaring cases as are given by way of examples could 
not occur in practice, errors precisely corresponding to them 
may, and often do, occur ; and produce much confusion of 
thought and error. 



Lesson xv.] definitions. 129 

§ 11. When you state the Genus that any Species belongs 
to, together with the Difference that constitutes it [* charac- 
terizes ' it, so as to separate it from the rest] you are said to 
give a ' Definition ' of that species. 

As, ' the Magnet,' (meaning, a na^itraZ-magnet) is defined 

* an iron-ore, having an attraction for iron : ' a ' Triangle,' a 

* three-sided figure : ' a ' Proposition/ ' an indicative ' [affirm- 
ing or denying ' Sentence.* ' Iron-ore ' — ' Figure ' — ' Sen- 
tence,' are evidently each the Genus, in these definitions re- 
spectively ; and the other part, the Difference, 

This is accounted the most perfect and proper kind of De- 
finition. And the two portions of which it consists — the 
*■ Genus ' and the ' Difference,' are called technically the 

* metaphysical parts : ' as not being two real parts into which 
any individual-object can be actually divided, but only differ- 
ent views taken [or notions formed] of a Class of objects, by 
our mind. 

What is called a * physical-definition,' is made by aa enu- 
meration of such parts of some object as are actually separa- 
ble ; such as are the Subject, Predicate, and Copula of a 
Proposition; — the root, trunk, branches, bark, &c. of a 
Tree, &c. 

A Definition which proceeds by enumerating several Prop- 
erties, — or, in the case of an individual — Inseparable-acci- 
dents, is called a ' Description ; ' or, according to some writers, 
an * Accidental-Definition.' 

It is evident that an Individual can be defined only by a 
Description ; that is, by stating the Species and (not ' Prop- 
erties ; ' since they belong to all the individuals of the Species ; 
but) the Inseparable-accidents. As 'Alexander the Great' 

Sp. 



would be described as ' a King ' ' of Macedon, who subdued 

Persia; ' ' Paris,' ' Tlie capital. . .City. . .of France.* 

§ 1 2. Definitions have also been distinguished — according 



130 SUPPLEMENT. \^Part III 

to the object designed to be effected by each, — into ' Nominal' 
and ' Real.' 

A Nominal-definition is usually described as being one 
which explains merely the meaning of the word defined ; 
and a Real-definition, that which explains the nature of the 
thing signified by that word. 

Now it may naturally occur to you to ask, are not thes.e 
(at least, in defining a Common-term) the same thing ? Since 
the object of our thoughts, when we employ a Common-term, 
is, (see above, Lesson VII. § 7,) — not any such really-exist- 
ing-\hmg as those imaginary abstract-ideas some speak of, but; 
— the Term itself, regarded as a ' Sign ' &c., as was formerly 
explained. 

And in many cases, accordingly, the 'Nominal' and the 
* Real ' definition do coincide. But by a Nominal-die^m.t\on 
is meant, (strictly speaking) one which expresses exactly 
what the Name itself conveys to every-one who understands 
that name : and nothing beyond this. And any Definition 
may be called (in a greater or less degree) a i?eaZ-definition 
which explains anything — more or less — beyond what is 
necessarily implied in the Name itself. 

Thus, any one who gives such an account of some one of 
the ' metals,' for instance, or of the ' Sun ' as modern research- 
es would enable him to give, would be advancing beyond a 
mere Nominal-definition ; since, in this latter, — the mere ex- 
planation of the words ' iron ' or ' sun ' — we, and our ances- 
tors 500 years ago, would coincide ; since both they and we 
use those words in the same sense ; though they knew much 
less than we do, of the nature of those things. 

In the case of strictly -5c^e?^<^/^c-terms, the Nominal and the 
Real-definition may be regarded as coinciding. Thus, the 
mathematical-definition of a circle, may be considered as sti'ict- 
ly ' Nominal,' inasmuch as it denotes precisely the same as 
the word ' Circle,' and nothing beyond ; every name being (in 



Lesson xv.] rules for defining. 131 

Mathematics) regarded as merely the ' definition abridged. 
And again, it may be regarded as so far a ' i?ea/-definition,* 
that it conveys all that can belong to the thing spoken of, since 
there can be no property of a Circle that is not in fact implied 
in the definition of a Circle ; or, which is the same thing, in 
the name, ' Circle.' It is, therefore, as much of a real-defini- 
tion as can, conceivably, be given, of a Circle. 

And, so with other scientific-terms. In respect of these, in 
short, the meaning of the name, and the nature of the thing, 
are one and the same. 

And accordingly, in Mathematics, the Definitions are the 
Principles from which our reasonings set out. 

On the other hand, since a ' diamond' or a * planet' or *a 
sheep ' &c. have, each of them (that is, each individual of any 
such Species) a real, actual existence in nature, independently 
of our thoughts, any of these may possess attributes not im- 
plied in the meaning we attach to the name ; and which are to 
be discovered by observations and experiments. Any expla- 
nation, however, of the nature of any object beyond what is 
implied in the signification of its" name, is not usually called a 
' Definition ; ' but the word ' Description ' is often used to de- 
note such an explanation. 

§ 13. What we are concerned with at present is 'Nominal- 
definition ; ' it being important, with a view to Reasoning, to 
ascertain the exact sense in which each Term is employed, 
and especially, to guard against any ambiguity in the Middle- 
term of any argument. 

The Rules [or cautions] commonly laid down in various 
treatises for framing a Definition, are very obvious : namely, 

i. That a Definition should be ' adequate ; ' i. e. compre- 
hending neither more, nor less, than the Term to be defined. 
For instance if, in a definition of ' Money ' you should specify 
its being ' made of metal,' that would be too narrow, as ex- 
cluding the shells used as money in some parts of Africa : if, 



132 SUPPLEMENT. \^Part in. 

again, you would define it as an ' article of value given in ex- 
change for something else,' that would be too wide, as it would 
include things exchanged by barter ; as when a shoemaker, 
who wants coals, makes an exchange with a collier, who wants 
shoes.* 

And observe, that such a defect in a Definition cannot be 
remedied by making an arbitrary exception; (such as was 
alluded to above, § 10,) as if, for instance, (and it is an instance 
which actually occurred,) a person should give such a Defini- 
tion of * Capital ' as should include (which he did not mean to 
do) ' Land ; ' and should then propose to remedy this by de- 
fining * Capital,' any ' property of such and such a description, 
except Land^ 

ii. The other caution usually given, is, that a definition 
should be clearer than the Term defined : clearer, that is, to 
the persons you are speaking to : since that may be obscure to 
one man, which is intelligible to another. 

And this rule evidently includes (what some give as a iiird 
rule) a caution against excessive prolixity, excessive brevity, 
and ambiguous language. 

* See Lesson I. on Money Matters. 



PART IV. 
FALLACIES 



LESSON XVL 



§ 1. Although sundry kinds of Fallacies have been from 
time to time noticed in the foregoing Lessons, it will be worth 
while to make some further observations thereon. 

By a * Fallacy ' is commonly meant ' any deceptive argument 
or apparent-argument, whereby a man is himself convinced, 
— or endeavors to convince others — of something which is 
not really proved.' 

Fallacies have been usually divided into two Classes ; those 
in the ybrm, and those in the matter: though the difference 
has not been in general clearly explained. 

The clearest way of proceeding will be to consider a ' Fal- 
lacy-in-form ' as one in which the Conclusion does not really 
follow from the Premises ; and a ' Fallacy-in-matter ' as one 
where the Conclusion does follow from the Premises, though 
there will be still something faulty in the procedure. 

In this latter case (where the Conclusion does follow) one 
may either object to the Premises as being ' unduly assumed,' 
or to the Conclusion as irrelevant ; that is, different, in some 
way, from what ought to have been proved, — namely, from 
what was originally maintained, — from what had been under- 
taken to be established, — from what the particular occasion 
requires, &c. 

These that have been mentioned (as the * Fallacies-in-form,' 
and * in matter ') must evidently include every possible Falla- 
cy ; since whatever objection can be brought against any ar- 
12 



134 FALLACIES. \_Part IV. 

gument or apparent-argument, must be an objection either 
against the Conclusion, or against the Premises, or against 
the connexion between the premises and conclusion ; that is, 
against the conclusiveness of the apparent argument. 

§ 2. ' Fallacies-in-form,' [in which the Conclusion does not 
really follow from the Premises] are such as we have already- 
given examples of, as violations of the rules above-ex- 
plained : such as ' undistributed-middle,' — ' illicit-process,' &c. 

Among others was noticed the fault of an ' equivocal Mid- 
dle-term,' taken in one sense in the one premise, and in a dif- 
ferent sense in the other. And since this Fallacy turns on 
the meaning of words, and not on the mere form in which the 
argument is expressed, some may be disposed to rank it rather 
under the Head of ' Fallacies-in-matter.' 

The most convenient course, however, will be to keep to 
the division already laid down ; and, accordingly, to reckon 
the Fallacy of ' equivocal-middle ' along with all the others in 
which the Conclusion does not follow from the Premises. 

And in truth the technical rules do apply to this, — the 
* Fallacy of equivocation ' — as soon as it is ascertained that 
the Middle-term is employed in two different senses, and con- 
sequently is, in reality, not one, but two terms. 

But of course the rules of Syllogism do not, alone, enable 
us to ascertain the meaning or meanings of any Term. That 
must be judged of from our knowledge of the subject-matter, 
— from the context, [or general drift of the discourse] — - an 1 
often from what we know or believe concerning the writer or 
speaker. 

And the same may be said, in many cases, in respect of not 
only the signification, but also the distribution or non-dis- 
tribution, of a Term ; on which depend the Fallacies of ' un- 
distributed-middle ' and ' illicit-process.' For when a Propo- 
sition is expressed indefinitely (as, ' Man invents arts ; ' ' Man 
is mortal;') we are left to judge from the subject-ma; vcr, 



Lesson xvi.] entiiymeme. 135 

&c., whether it is to be understood as Universal or as Par- 
ticular. 

And again, the sign ' all,' which, in an Affirmative proposi- 
tion, denotes Universality) in a Negative-proposition, general- 
ly, though not invariably, indicates a Particular ; that is, usu- 
ally, though not always, the negation is understood as a negation 
of universality. For instance, of these two propositions, ' all 
they that trust in hira shall not be confounded,' and ' we 
shall not all sleep,' the one would be understood as Universal, 
and the other as Particular. 

Observe, also, that the sign ' all ' is sometimes understood 
as meaning ' ail-collectively ; ' sometimes ' every -one, sepa- 
rately^ As ' all the apples on that tree are enough to fill a 
bushel : ' i. e. all together : and ' they are all ripe ; ' i. e. 
every one, 

§ 3. You are to observe that we cannot always decide ab- 
solutely as to which Class we should pronounce some particular 
fallacy to fall under, those in ' form,' or those in ' matter : ' 
because it will often happen, when an argument is stated 
(which is usually the case) as an Enihymeme, that the suppressed 
premise may be either one which is false, but which would, if 
granted, make the Syllogism complete : or else one which is 
true, but which would not complete a regular Syllogism. 
Now, on the former supposition, the Fallacy would be in the 
^matter; ' on the other supposition, it would be in the '■form^ 

For instance, in this Enthymeme, ' The Country is dis- 
tressed ; therefore it is misgoverned,' we cannot decide abso- 
lutely whether the premise meant to be understood, is 'every 
Country that is distressed is misgoverned ; ' which would make 
the syllogism correct, but would not be admitted as true ; or, 
' every Country that is misgoverned is distressed ;' which would 
leave the Middle-term undistributed. 

And again, when both Premises are expressed, it will often 
happen (as in an example formerly given) that we have the 



136 FALLACIES. [^Pait IV. 

alternative of eitlier denying tlae trvih of one of the premises, 
— supposing the Middle-term used in the same sense in both, 
■ — or denying the conclusiveness of the argument, supposing 
the Middle-term used in eax)h premise in such a sense as to 
m.ake that premise true. If by ' cmitrary to experience ' you 
mean two different things, in the two premises, respectively, 
then, each is, by itself, true, but they prove nothing : if you 
mean by it the same in both premises, then, one of them is 
untrue. 

§ 4. But observe, that when you mean to charge any argu- 
ment with the fault of ^ equivocal-middle,' it is not enough to 
say that the Middle-term is a word or phrase which admits 
of more than one meaning ; (for there are few that do not) 
but you must show, that in order for each premise to be ad- 
mitted, the Term in question must be understood in one sense 
(pointing out what that sense is) in one of the premises, and 
in another sense, in the other. 

And if any one speaks contemptuously of * over-exactness ' 
in fixing the precise sense in which some term is used, — of 
attending to minute and subtle distinctions, &c., you may reply 
that these minute distinction's are exactly those which call for 
careful attention ; since it is only through the neglect of these 
that Fallacies ever escape detection. 

For a very glaring and palpable equivocation could never 
mislead any one. To argue that ' feathers dispel darkness, 
because they are light^ or that ' this man is agreeable, because 
he is riding., and riding is agreeable,' is an equivocation which 
could never be employed but in jest. And yet, however slight 
in any case may be the distinction between the two senses of 
a Middle-term in the two premises, the apparent-argument 
will be equally inconclusive ; though its fallaciousness will be 
more likely to escape notice. 

Even so, it Is for want of attention to minute points that 
houses are robbed, or set on fire. Burglars do not in general 



Lesson xvi.] equivocation. 137 

come and batter down tlie front-door ; but climb in at some 
window whose fastenings have been neglected. And an in- 
cendiary, or a careless servant, does not kindle a tar-barrel in 
the middle of a room, but leaves a lighted turf, or a candle- 
snuff, in the thatch, or in a heap of shavings. 

In many cases, it is a good maxim, to ' take care of little 
things, and great ones will take care of themselves.' 

§ 5. Of the Fallacies of ' undistributed-middle ' and of ' il- 
licit-process,' &c. (which have been formerly explained) no 
more need be said in this place. 

But in respect of the ' Fallacy of equivocation,' it is worth 
while to notice briefly some of the different modes in which a 
word or phrase comes to be employed in several senses. 

i. That maybe reckoned an accidental equivocation, in which 
there is no perceived connexion between the different senses. 
Thus ' pen ' is an instrument for writing, or an enclosure for 
cattle ; ' turtle ' a kind of bird, and a kind of tortoise ; and 
' case ' is used (as was noticed in Lesson VII. § 3,) in three 
senses. Of this kind is the ambiguity of several proper- 
names (as John, Thomas, &c.) also noticed in the same 
place. 

ii. There are several words which are ambiguous from be- 
ing employed in what is technically called a ''jirst intention ' 
and a * second intention J 

A ' Second-intention ' of any word is that signification which 
it bears in reference to some particular art, science, study, 
pursuit, or system ; and its first-intention is its ordinary collo- 
quial sense when there is no such reference. 

Thus, the ordinary signification of the words ' ship,' ' beast,* 
and ' bird,' every one knows ; but sailors limit the word ' ship 
to vessels of a certain construction ; ' beast ' is the word ap- 
plied by farmers in some parts, especially, and exclusively, to 
the ' ox-tv\hQ ; ' and ' bird ' is used in a ' Second-intention ' to 
signify 'partridge,' 

12* 



138 FALLACIES. [^Pttrt IV 

§ 6. It is evident that a word may have several different 
' Second-intentions,' according to the several systems, &c. 
into which it may be introduced as one of the technical-terms. 

Thus ' line ' is technically employed in Geometry, in Ge- 
ography, in the Military-art, in the art of Angling, in Print- 
ing, &c. 

The word ' Species ' is employed by Naturalists in a cer- 
tain ' Second-intention ' when they are speaking of organized- 
beings. 

The ordinary sense [' first-intention '] of the word, is that 
which has been explained in these Lessons : but Naturalists 
restrict it to such a class of animals or plants as are supposed 
to have descended from a common stock. 

In ordinary discourse any one would say that a ' Grey- 
hound ' or a 'Mastiff' is a kind [' Species'] of dog: but a 
Zoologist would say (in technical language) that these are 
only ' Varieties,^ and that all dogs are of one Species. So 
also, in common discourse any one would speak of ' Cauli- 
flower,' and several others, as ' kinds ' of ' Cabbage : ' but the 
Botanist reckons all these as ' varieties ' of the single Spe- 
cies, Cabbage. 

Those, in short, which are (in the technical language of 
these Lessons) the ' lowest-Species ' that the Naturalist treats 
of, are called by him, not Species, but Varieties ; and again 
those classes under which his Species come, he never calls 
Species of a higher Genus, but Genera, Orders, &c. 

Much confusion of thought has often arisen from over- 
looking this technical-sense [' second intention '] of the word 
* Species.' 

In some instances the ' second-intention ' [or philosophical 
sense] of a word, is, — instead of being more limited, — more 
extensive than the ' first-intention ' [or, popular sense.] 

Thus ' affection,' which is limited, in popular use, to * love,' 
is employed by i)hilosophers as comprehending both ' benevo- 



Lesson xvi.] analogy. 139 

lent and malevolent afFections/ So also ^ charity,' which is 
often, in popular use, confined to ' almsgiving ' — ' flower,' to 
such flowers as have ' conspicuous petals,' — and ' fruit ' to 
such fruits as are ' eatable,' have each a technical second- 
intention, which is more extensive. 

§ 7. iii. A word will often be employed to denote (in dif- 
ferent senses) to things which have a ' resemblance^ or ' anal- 
ogy^ to each other. 

A ' blade,' of grass, or of a sword, have the same name from 
the direct resemblance between the things themselves. But 
instances of this kind are far less common than those in 
which the same name is applied to two things, not from 
their being themselves similar, but from their having similar 
relations to certain other things. And this is what is called 
' Analogy.' 

Thus, the ' sweetness ' of a * sound ' and of a ^ taste ' can have 
no resemblance : but the word is applied to both, by analogy, 
because as a ' sweet ' taste gratifies the palate, so does a ' sweet ' 
sound, the ear. 

Thus also we speak in the * secondary ' [or ' transferred,' 
or * analogical '] sense of the ' hands ' of a Clock — the ' legs ' 
of a Table, — the ' foot ' of a Mountain, — the * mouth ' of a 
River, &c. which words in their * primary ' [' proper,' or orig- 
inal] sense, denote the * hands ' of a man, — the * legs, foot, 
and mouth ' of animals ; from the similar relations in which 
they stand to other thin^, respectively, in reference to use, 
position, action, &c. 

The words pertaining to Mind may in general be traced up, 
as borrowed (which no doubt they all were, originally) by 
Analogy, from those pertaining to Matter : though in many 
cases the primary sense has become obsolete. 

Thus, ' edify^ ' in its primary sense of ' build upf ' is dis- 

* Sec Peter, i. ch. 2, v. 5. t See Johnson's Dictionary. 



140 FALLACIES. [^Part IV 

used, and the origin of it often forgotten ; although the sub- 
stantive ' edifice ' remains in common use in a corresponding 
sense. 

When, however, we speak of ' weighing ' the reasons on 
both sides, — '• of ' seeing,' or ' feeling ' the force of an argu- 
ment, — ' imprinting ' any thing on the memory, &c. we are 
aware of these words being used analogically. 

It is an analogical sense that ' Division,' ' Part,' and 
several other technical terms have been employed in these 
Lessons. 

§ 8. There are two kinds of error, each very common — 
which lead to confusion of thought in our use of analogical 
words : 

i. The error of supposing the things themselves to be similar, 
from their having similar relations to other things. 

ii. The still commoner error of supposing the Analogy to 
extend further than it does ; [or, to be more complete than it 
really is ;] from not considering in what the Analogy in each 
case consists. 

For instance,- the ' Servants ' that we read of in the Bible, 
and in other translations of ancient books, are so called by 
Analogy to servants among us : and that Analogy consists in 
the offices which a ' servant ' performs, in waiting on his mas- 
ter, and doing his bidding. It is in this respect that the one 
description of ' servant ' ' corresponds ' [' answers'] to the other. 
And hence some persons have been led to apply all that is 
said in Scripture respecting Masters and Servants, to these 
times, and this Country : forgetting that the Analogy is not 
complete, and extends no further than the point above-men- 
tioned. For the ancient ' servants,' (except when expressly 
spoken of as /<!^Ve(^servants) were Slaves ; a part of the IVIas- 
ter's possessions. 

§ 9. iv. A word will often (in different senses) be applied 
to two things, eonnectcd, not by Ivesemblance or Analogy, but 



Lesson XVI.] ANALOGY. 1 1 J 

by the circumstance of time or place, as being ' Cause and 
EfFect/ or ' Part and Whole,' &c. 

Thus, when we say, ' the fire gives heat,' and * I feel heat,' 
it is plain that the ' heat ' of the fire is not a sensation in the 
fire, and cannot resemble or be analogous to a sensation ; but 
is the cause of the ' sensation ' of ' heat ' in me. 

This kind of transfer of a word from its ' primary ' to a 
Secondary sonse, is called ' Metonymy.' It is thus we speak 
of a ' Crown,' or a ' Throne ' for ' regal-power ' ' the sword,* 
for * war ; ' a * voice,' for a ' declaration ; ' and a man is said 
to be ' worth ' such and such a sum of money ; meaning that 
he posseses property that is worth so much, &c. 

Much confusion of thought, and many Fallacies, have arisen 
from inattention to this source of ambiguity.* It seems strange, 
but it is quite true, that things have often been in this way 
confounded together, which have not the least resemblance or 
analogy to each other. 

A remarkable instance of this is to be found in the ' pri- 
mary ' and ' secondary ' uses of such words as ' same ' — ^ one ' 
— ' identical,' &c. In the primary sense they imply ' numer- 
ical unity,' [individuality] and do not imply, necessarily, any 
similarity. For when we say of any grown man that he is 
the ' same person ' whom we remember to have seen when an 
infant, this is, not from his now resembling an infant. Another 
infant, now, would be much more like what he then was. 

In the secondary sense, on the other hand, these words 
imply nothing hut exact — or nearly exact — similarity. For 
instance, if a man finds in a mine some metal which turns out 
to be gold with a small alloy of copper, he would say, it is the 
same metal of which coins, or of which watches are made : 



* The ambiguity of the word ' Division,' when used to signify one 
of the portions into which anything is divided (See Lesson XV., § 6,) is of 
this kind. 



142 FALLACIES. [Part IV. 

not meaning, of course, that one single piece of metal car 
be in two places at once ; but only, that there is a perfect 
similarity. 

So, also, several persons are said to be in one and the same 
posture, when they are all placed alike ; and to have * one and 
the same ' idea in their minds, when they are all thinking 
alike. (See Lesson VII. § 8.) 

§10. Now the mode in which these words have been thus 
transferred (to the utter bewilderment of the inattentive) is 
this : one single word, — such as ' gold,' or ' man,' or ' tri- 
angle,' or ^ fever,' — will equally well apply to any one piece 
of gold, or individual man, or triangle, or fever, &c. And so 
also will one single Definition [or Description] of a triangle r 
and hence the things themselves come to be called ' owe,' — 
— the ' same^ ' identical,' &c., because all the individuals thus 
named or described, are (according to the modern phrase, 
which is very correct) * of the same description' 

In the transferred [secondary] sense, accordingly, you may 
observe, that things are often spoken of as ' very nearly the 
same, but not quite ;' there being some small difference be- 
tween them. In the ' primary ' sense on the other hand, 
* unity,' — * identity ' &c. do not admit of degrees. For in- 
stance, ' This man ' either is or is not the same person whom^ 
I saw formerly when he was an infant or child ; and that, 
whether he differ much or little, from what he then was. 

But what helps to introduce confusion, is, that * identity' 
in the primary sense, is in many cs^sesjudged of, and inferred, 
from similarity. For instance, a man may be ready to swear 
to some picture as the one which he had lost, ^rom his per- 
ceiving a perfect similarity; and yet it might, perhaps, be 
afterwards proved to his satisfaction, that it was not that one, 
but an exact copy. 

§ 11. Besides the causes of ambiguity that have been just 
mentioned, it is to be observed that there are several words 



Lesson xvi.] ^ ellipsis. 143 

which it is customary to employ elliptically ; that is, in com- 
bination with something understood ; and that men are apt to 
forget when it is that such a word is used with, and when 
without, this ellipsis. 

For instance, we speak of such a one possessing £10,000 ; 
(though, perhaps, he may not actually possess ten pounds in 
money) meaning, that his whole property would exchange for 
that sum. And, ordinarily, such a mode of speaking leads 
to no practical inconvenience. But there is no doubt that 
it has contributed to foster that enormous practical error 
known among Political Economists * as the ' Mercantile 
System.' 

So also we speak commonly of * the example of such a one's 
punishment serving to deter others from crime.' And usu- 
ally, no misapprehension results from this, which is, in truth, 
an elliptical expression. But sometimes sophistical reasoners 
take advantage of it, and men who are not clear-headed are 
led into confusion of thought. Strictly speaking, what deters 
a man from crime, in such cases as those alluded to, is, the 
apprehension of himself suffering punishment. That appre- 
hension may be excited by the example of another's being 
punished ; or it may be excited without that example, if pun- 
ishment be denounced, and there is good reason to expect 
that the threat will not be an empty one. And on the other 
hand, the example of others suffering punishment does not 
deter any one, if it fail to excite this apprehension for him- 
self; if, for instance, he consider himself as an exempt per- 
son as is the case with a despot in barbarian countries, or 
with a madman who expects to be acquitted on the plea of 
insanity. 

So also, when any one speaks of being in distress from be- 
ing * out of work^ and of his ' seeking for employment^ we 

* See Seniors and Whatelv's Lectures on Political Economy. 



144 FALLACIES. [Part iv. 

understand him to mean ' work by which he can earn a sub- 
sistence/ But great errors have often been committed by 
writers who have lost sight of the elliptical character of the 
expression, till they have practically forgotten in their rea 
sonings that the thing really desired is, not the laior, but the 
(/ain. 

To this head may, perhaps, be referred the ambiguity 
(which has been a source of endless confusion) formerly no- 
ticed (Lesson II.,) of such words as 'because,' &c., and again 
' therefore,' and several others. 

When, in accounting for the wetness which I perceive on 
the ground, I say, ' the ground is wet because it has rained,' 
I mean (speaking at full length) to assign the ' rain ' as the 
' cause of the wetness : ' when, again, I infer that ' it has rained 
because the ground is wet ' the meaning of the word * because ' 
is, if fully expressed, that I assign the wetness as the ^ cause, 
of my belief 

The same may be said of such words as * may,' ' possible,' 
&c., and again, ' must,' ' necessary,' &c. (See Lesson X., 
§8.) 

When I say of a man forcibly carried off by enemies, ' he 
must go wherever they conduct him,' I mean, ' he cannot avoid 
going : ' when I say that on his release ' he must eagerly re- 
turn to his home,' I mean that ' / cannot avoid drawing that 
conclusion^ 

So also, if I say of a man in health and at liberty, * he may 
go out or stay within,' I mean that neither going nor staying 
is unavoidable to him : but when I say of a man who is sick, 
that ' he may recover,' I do not mean (as in the former case) 
that * this depends on his choice," but that ' I am not led una- 
voidably to the conclusion, that he will recover, or that he will 
not recover.' 

§ 12. There are also other ways in which a Term may be 
so modified in its sense as not to have precisely the same 
meaning in both premises. 



Lesson xvi.] fallacies-of-division. 145 

For you are to remember that even any one word which is 
not itself one of the Terms, but only a small portion of one of 
them, may be so understood as to affect the sense of the whole 
Terra. Even a difference in the position of a word in respect 
of the rest, may greatly alter the sense. 

For instance, ' He who believes his opinion always right, 
deems himself infallible ; you always believe your opinion 
right ; therefore you deem yourself* infallible.' Here, the 
premises are both true ; for any opinion which you did not 
believe to be right, would plainly not be your opinion ; and it 
would be difficult to deny that a man considers himself infalli- 
ble, who should believe that his opinion is uivariably right. 
But the different situation of the word ' always ' gives a differ- 
ent sense to the Middle-term in the two premises. To ' think 
your opinion always right,' means, to have a general convic- 
tion respecting the lohole of your opinions collectively, that 
none of them is ever wrong : but ' always to think your opin- 
ion right,' means, ' to have a particular conviction, on each 
occasion, separately, that your opinion, on that occasion, is 
right.' 

A Fallacy of this character, — that is, where the Middle- 
term is taken collectively in one premise, and dividedly in the 
other, — is technically called the ' Fallacy-of-c?m5iow,' or of 
' composition ; ' according as the Middle-term is understood in 
a collective-sense in the it/o; or- premise, and in a divided-sense 
in the Minor ; or vice versa. 

A glaring example would be * all the apples from that tree 
are worth 205. ; this is an apple from that tree ; therefore it is 
worth 2O5.' 

Such a fallacy has helped to give plausibility to what has 
been called ' the doctrine of necessity.^ For instance, ' He who 
necessarily goes or stays ' (in reality, ' who necessarily goes, 
or again, who necessarily stays ') is not a free-agent ; you 
necessarily go or stay ; (that is, — taking these two things in 
13 



146 FALLACIES. \Part iv. 

connection, — you ' necessarily take the alternative ') ' there- 
fore you are not a free agent.' 

§ 13. The way in which this Fallacy usually occurs in 
practice, is, when something is proved separately concerning 
each one of several things belonging to some class ; and then 
this is considered as having been proved concerning the whole 
class collectively ; that is, concerning those things taken in 
connexion with each oth$r. 

A man, for instance, swallows a certain drug, and is seized 
with alarming symptoms : you show that these symptoms may 
possibly have arisen from other causes: the same drug is 
swallowed by another man, who is seized with like symptoms ; 
and you show that other causes may have produced the symp- 
toms in him : the same may be shown, suppose, in each separate 
case (considered each by itself) out of 100 ; and then you 
assume that it has been proved that all the men who have 
taken the drug and exhibited like symptoms may have been 
affected, all of them, by natural causes. 

This kind of argument has been employed to refute the ac- 
counts given by the Evangelists of the miracles they record ; 
that is, explaining some one of the recorded cures — considered 
by itself, as an accident ; and then the same with another, and 
another ; and so on. 

Sometimes again a Middle-term is ambiguous from being 
understood in one premise in conjunction with certain circum- 
stances actually pertaining to it, at a particular time, &c., and, 
in the other premise, independently of those circumstances. A 
glaring example would be, if any one should pretend to prove, 
(which would of course be only as a jest,) that because what 
you have on your back was the covering of a sheep, therefore 
the sheep wore a coat of blue or red broadcloth. This is called, 
in the technical language of the Latin treatises, ' Fallacia 
accidentis.' 

It is evident that when any ambiguity, of whatever kind, in 



Lesson xvi.] irrelevant-conclusion. 147 

a Middle-term, is suspected, the natural course is to seek for, 
or to demand, a Definition of it. Only, remember that it 
would be impertinent to insist, in every such case, on a com- 
plete definition, beyond what is requisite for removing any 
douht as to the argument before us ; i. e. as to the Middle-term's 
being employed in the same sense in both premises. 

For instance, if there were a discussion respecting a person's 
having swallowed ^ poison,^ and some ambiguity connected with 
the reasoning, were suspected in the employment of that 
word, it would not be necessary to give a definition such as 
should extend to ' every poison,' including such as savages use 
for their arrows : because the supposed question relates only 
to poisons taken into the stomach. 

§ 14. The Faliacies-in-matter are divided (as has been 
said) into two kinds : ' undue-assumption-of-a-premise,^ and 
' irrelevant-conclusion,^ 

It is to be observed that no one is to be charged wiih/alla" 
c^ows-proceeding merely because he argues from Premises 
which we deny ; or because the Conclusion he draws is not 
the one we would wish to see proved. For neither of these 
implies any deception. 

One man may assume facts or principles which another will 
not admit ; but provided he does this openly and knowingly, 
there is no Fallacy in the case. 

Or again, we may, (suppose,). wish to have it pointed out 
and proved who is the perpetrator of such and such a crime ; 
but if the accused party prove that it was not he, we have no 
right to demand more. 

But if any one is convinced by an argument based on some 
Premise which he would not have admitted if distinctly put 
before him, there is in this case a Fallacy. 

And so there is, if any one is satisfied, or endeavors to sat- 
isfy others, by proving some conclusion different from what 
he had originally maintained ; or from what was originally 



148 FALLACIES. \^Part IV. 

proposed as the Question : or, (which comes to the same) 
which is the contradictory, not, of what he had originally de- 
%ied^ but of some different proposition. This is properly the 
i<"'allacy of ' irrelevant-conclusion.' 

§ 15. Under the former of these two classes of Fallacy 
tx)mes what is, technically, called ' begging the Question ; ' 
that is, assuming as a Premise the very Proposition which, — 
Ia other words, — is proved as the Conclusion. The way in 
wliich this is usually done is that which is commonly called 
* p^rguing in a circle ; ' that is, proving some conclusion by 
mt^ans of a Premise which is itself deduced — more or less 
remotely — from premises deduced from that very Conclu- 
sion, assumed as a Premise. As if you were to prove that A 
is B, because C is D ; and that C is D, because E is F ; and 
so on, till at length you come to infer that Y is Z because 
A is B. 

Of course the narrower the Circle, the less likely it is to 
escape the detection, either of the reasoner himself, (for men 
often deceive themselves in this way) or of his hearers. When 
there is a long circuit of many intervening propositions before 
you come back to the original Conclusion, it will often not be 
perceived that the arguments really do proceed in a ' Circle.* 
Just as when any one is advancing in a straight line (as we 
are accustomed to call it) along a plain on this Earth's sur- 
face, it escapes our notice that we are really moving along the 
circumference of a Circle^ (since the earth is a globe) and 
that if we could go on without interruption in the same line, 
we should at length arrive at the very spot we set out from. 
But this we readily perceive, when we are walking round a 
small hill. 

For instance, if any one argues that you ought to submit to 
the guidance of himself, or his leader, or his party, &c. because 
these maintain what is right ; and then argues that what is so 
maintained is right because it is maintained by persons whom 



Lesson xvi.] fallacy-in-matter. 149 

you ought to submit to ; and that these are, himself and his 
party ; or again, if any one maintains that so and so must be a 
thing morally wrong, because it is prohibited in the moral 
'portion of the Mosaic-law, and then, that the prohibition of it 
does form a part of the moral (not the ceremonial, or the civil) 
portion of that Law, because it is a thing morally wrong^ — 
either of these would be too narrow a Circle to escape detec- 
tion, unless several intermediate steps were interposed. And 
if the form of expression of each Proposition be varied every 
time it recurs, — the sense of it remaining the same, — this 
will greatly aid the deception. 

Of course, the way to expose this Fallacy, is to reverse this 
procedure : to narrow the Circle by cutting off the interme- 
diate steps ; and to exhibit the same proposition, — when it 
comes round the second time, — in the same words. 

§ 16. In all cases, an unduhj-assumed premise (i. e. one 
which would not be admitted if clearly stated, and deUberately 
considered) is the more likely to escape detection, the longer 
the train of argument is, and the greater the number of well- 
established propositions introduced. When this artifice is 
employed, a dull or thoughtless hearer is apt to say, ' there is 
much truth in what has been urged.' And so, perhaps, there 
is. There may have been introduced, in the course of the 
reasoning, twenty propositions, all of them true, except one : 
the denial of which one would nullify the whole train of argu- 
ments. A chain which has 07ihj one faulty link, is not indeed 
the stronger, but is the more likely to appear strong, by the 
addition of a great many sound links. 

It also contributes to this kind of deception, to suppress the 
unduly-assumed premise ; stating the argument as an Enthy 
memo expressing the true premise, and giving proofs of the 
truth of that, as if everything turned on the establishment of 
that premise. 

So also, in Fallacies of the other class, — the ' irrelcvant- 
13* 



150 FALLACIES. \_Part IV. 

conclusion ' — it often aids the deception, to suppress the Cbw- 
clusion itself: bringing forward ai'guments which do indeed 
go to prove a Conclusion, somewhat like the one required, 
though not the very one : and then (instead of expressly stat- 
ing the conclusion that really does follow, or again, that which 
had been originally maintained) a man will say ' the inference 
from this is plain : or ' I have thus established my point ; * 
or the position of our opponents is thus completely over- 
thrown,' &c. 

§ 17. The two kinds of ' Fallacy-in-Matter,' are very com- 
monly combined in one course of argument : that is, a false or 
a doubtful premise will be assumed as having been proved by 
arguments which go to prove, not that, but another proposi- 
tion, somewhat like it. 

For instance, instead of proving that * this Prisoner has 
committed an atrocious fraud,' you prove that ' the fraud he is 
accused of is atrocious : ' instead of proving (as in the well- 
known tale of Cyrus and the two coats) that ' the taller boy 
had a right to force the other boy to exchange coats with him,' 
you prove that ' the exchange would have bsen advantageous 
to both : ' instead of proving that ' a man has not the right to 
educate his children or to dispose of his property, in the way 
he thinks best,' you show that the way in which he educates 
his children, or disposes of the property, is not really the 
best : instead of proving that ' the poor ought to be relieved 
in this way rather than in that,' you prove that the poor ought 
to be relieved ;' instead of proving that ' an irrational-agent — 
whether a brute or a madman — can never be deterred from 
any act by apprehension of punishment,' (as for instance a dog, 
from sheep-biting, by fear of being beaten) you prove that 
* the beating of one dog does not operate as an example to 
other dogs,' &c., and then you proceed to assume as prem- 
ises, conclusions different from what have really been estab- 
lished. 



Lesson xvi.] fallacy-in-matter. 151 

The chief difficulty in detecting any Fallacy of whatever 
kind, in our own reasonings, or another's, arises (as was for- 
merly remarked) from its being usually stated in an oblique, 
indirect, and somewhat inverted and perplexed form of ex- 
pression ; and more especially when diluted, as it were, with 
a multitude of words : just as poison is more likely to escape 
detection when disguised and diluted by being mixed up with 
a quantity of innocent ingredients, than when presented in a 
small concentrated dose. 

The validity, or the fallaciousness, of any course of reason- 
ing, will then be made the most evident, when examined ac- 
cording to the foregoing rules, after laying aside all redundant 
words put in for mere embellishment of style, and stating the 
whole in the most simple language, and in regular order, as 
briefly as is compatible with perfect clearness. 



PART V. 
DIFFERENT KINDS OF ARGUMENTS. 



LESSON xvn. 



§ 1. It remains to make a few remarks on the ^finding 
[according to the Latin writers, Invention~\ of arguments ; ' 
the foregoing Lessons relating only to the rules for passing 
judgment on arguments. 

It is to be observed, in the first place, that the words 'infer* 
and ''prove,^ (which we have frequently had occasion to em- 
ploy) denote, not, two different things, but the same thing 
considered in two different points of view. He who ' infers ' 
(correctly) proves ; and he who ' proves ' infers : and yet the 
two expressions are not synonymous. 

So also, the 'road from London to Liverpool' and the 
* road from Liverpool to London,' are rot diiFerent things ; 
but the one expression calls to mind the thought of a journey 
from the Metropolis to the Seaport ; and the other, the re- 
verse. And in like manner, the word ' infer ' fixes the mind 
first on the Premises and then on the Conclusion ; the word 
prove,' on the contrary, leads the minds y^'om the Conclusion 
(in this case called the ' Question ') to the Premises. 

Hence, we say commonly ' what do you infer from that ? ' 
■ How do you prove this ? ' namely, this Conclusion. 

And the corresponding Substantives are often used to denote 
that which is, in each instance, last in the mind : ' inference ' 
being often used to signify a Conclusion [Proposition-inferred,! 
and ' proof,' a Premise. 



Lesson xvii.] different kinds of arguments. 15S 

When, then, any long train of reasoning is carried on, we 
proceed — in ' inferring,' and in * proving ' — in opposite di- 
rections : our object being, in the one case, to ascertain from 
all that we know on a certain subject, what Conclusion is to 
be drawn ; and in the other case, — when we are satisfied as 
to the Conclusion — to consider by what arguments we shall 
estabhsh it. 

§ 2. In the former case, from established * data ' [certain 
known facts, and acknowledged principles] we infer so and so ; 
and from this conclusion, in conjunction with other known 
truths, we infer something else ; and so on, till we have ascer- 
tained what is decisive of the question before us, or as much 
as we are able. 

In the latter case, we proceed upwards from the Premises 
which will establish the Conclusion we are maintaining, to 
the arguments which will prove those Premises : and so on, 
till we arrive at something that is admitted. And from this, 
— when we have to convince others — we generally proceed 
through the same train of reasoning, in a reversed order, 
downwards, till we have arrived at the Conclusion to be es- 
tablished. 

AYe are sometimes then employed in what may be called 
* seeking for a Conclusion^ and sometimes again, in * seeking 
for Middle-terms.^ 

For instance, a Judge is inquiring whether the estate does, 
or does not, belong by law to the claimant : the Suitor (or his 
Advocate) is seeking for proofs that the estate is his. The 
Natural-philosopher, when investigating, inquires, ' what is 
the cause of the tides ; ' the Physician, ' what is this patient's 
disease;' and each, when he has satisfied himself, and is 
proceeding to teach or to convince others, sets himself, — like 
the Advocate, — to seek for proofs; sometimes employing 
the same that had led himself to the conclusion, and some- 
times different ones ; according to what he judges will serve 



154 DIFFERENT KINDS OF ARGUMENTS. \_Part V. 

best to satisfy the understanding of others, that ' the cause of 
the tides is so and so ; ' or that ' such and such is the patient's 
disease.' 

And in thus laying before others this process of reasoning, 
a man will sometimes proceed in the same order in which he 
had sought for the arguments, (that is, beginning from the 
Conclusion, and proceeding upwards) or again, sometimes, 
in the reverse order ; setting out from something that is ad- 
mitted, and proceeding downwards, towards the ultimate Con- 
clusion.* 

§ 3. In treating of the operation of seeking for Middle- 
terms — in other words, for Arguments to establish, on each 
occasion, the Conclusion maintained — we are naturally led 
to inquire concerning the different kinds of Arguments one 
often finds alluded to in books, or in conversation. 

These are in general very indistinctly described, and con- 
fusedly enumerated. 

We hear persons speaking of ' Syllogistic reasoning,' and 
such as is not ' Syllogistic ; ' — of Categorical, or Hypotheti- 
cal Arguments,' — of 'Demonstrative, and Probable' [or 
Moral] Reasoning ; of ' Direct and Indirect Arguments ; ' — 
of A priori Arguments,' ' Arguments from Testimony,' — from 
* Analogy,' — from ' Example,' — by ' Parity-of-reasoning,' 
&c., without any distinct account being given of these and other 
modes of procedure. 

In reality, to enumerate thus confusedly the several kinds 
of Argument, is to commit the fault formerly noticed in refer- 
ence to ' cross-divisions ; ' there being, in this instance, no less 
than four different divisions ; which ought not to be blended 
together. 

ist. The division of Arguments into irregular and syllo- 
gl^tic, and of Syllogisms again, into Categorical and Hyj.>o- 



* See the notice in Lesson IX. of the Analytical and Synthetical oulor. 



Lesson xtii.] different kinds op arguments. 155 

thetical, &c. is a division, strictly-spealving, not of Arguments 
themselves, but of ih^ forms of stating an argument. For it 
is manifest (as above explained) that one individual argument 
may be stated either in a Hypothetical or in a Categorical 
form, and in the first figure, or in the second, &c. 

illy. The division of Arguments into proiahle and demon* 
strative, is evidently according to the subject-matter : and is, 
strictly, not a division of Arguments, considered as Arguments, 
but rather, of the Propositions they consist of, in respect of 
the ' matter ' of those Propositions. 

§ 4. iiird. Arguments are divided into ' direct ' and ' indi^ 
rect, according as your object is to establish either the truth of 
the Conclusion, or the falsity [the ' Contradictory '] of one of 
the Premises. For when we arrive, by sound reasoning, at a 
false Conclusion, it is plain that one at least of the Premises 
must be false. 

In short, every valid Argument may be stated in the form 
of a Conditional-Proposition : ''If the Premises are true, the 
Conclusion is true : ' then, supposing you admit the Premises 
to be true, you must admit the truth of the Conclusion : 
(which corresponds to a Constructive Conditional-syllogism) 
and hence, also, supposing you find the Conclusion false, 
you must admit that the Premises, or one of them, cannot 
but be false ; since if they were both true, the Conclusion 
would be true : and this corresponds to a Destructive Condi- 
tional-syllogism. 

Now the above is evidently a Division, not, strictly speak' 
ing, of Arguments, but of the purposes for which any Argu- 
ment may be designed : namely, either to prove its Conclu- 
sion, or to c?*5prove one of its Premises. 

For the same individual Argument may answer both pur- 
poses, to different persons. For instance, ' Whatever is main- 
tained by the Stoics (or by such and such a philosopher, sect, 
party, &c.) must be admitted ; that pain is no evil (or such 



156 DIFFERENT KINDS OF ARGUMENTS. \_Part V. 

and such a doctrine, whatever it may be, in each instance) is 
so maintained ; therefore this must be admitted : ' now a zeal- 
ous partizan will be so fully convinced of the Premises that 
he will assent to the Conclusion : others may be so revolted 
by the Conclusion, that they will thereupon reject the Major- 
premise. 

The Argument, therefore, will, to the one, be ' direct,' and 
to the other ' indirect.' 

§ 5. ivly. When we speak of arguing from a Cause to an 
Effect, or of arguing from Testimony to the truth of what is 
attested, or again, from a known case to an unknown similar 
case, &c. these kinds of Argument are distinguished from 
each other 'according to the relation existing between the 
Premises and the Conclusion, in respect of the subject-matter 
of each.' 

This, then, and this alone, is properly a division of Argu- 
ments, as such. 

When we say, for instance, that in arguing from the ' fall 
of rain ' to the consequent ' wetness of the roads,' the Premise 
is a Cause, and the Conclusion drawn, an JEffect, it is evident 
we are not speaking of the mere syllogistic connexion of the 
Premise and Conclusion ; (which, as was formerly explained, 
is always the same) nor again are we speaking of the subject- 
matter of those Propositions (as in the iid Head) considered, 
— each by itself, — merely as Propositions, independently of 
the Argument : for ' Cause,' and ' Effect ' are relative words ; 
and the Premise is called a Cause of that Effect which is 
inferred in the Conclusion. So that it is the relation, in re- 
spect of matter, of the Premise to the Conclusion, that we are 
speaking of. 

And so also in respect of Arguments from Testimony, and 
the other kinds that have been alluded to. 

§ 6. Arguments, then, may be divided, first, into two class- 
es : ist. such as might have been used to account for the Con- 



Lesson XVII.] two classes of arguments. 157 

elusion, supposing it had been already granted ; and iili/, those 
4 which could not. Or, in other words, ist. Arguments from 
Cause to Effect ; and lily, all other kinds. 

For instance, if I infer from ' a fall of rain,' that ' the roads 
must be wet,' I am using an Argument of the former Class ; 
[an ' A-priori- Argument '] since if it were known, and re- 
marked by any one, that the roads are wet, I should account 
for that fact by informing him that it had rained. 

Or again, if a person were known to have committed a mur- 
der, and it were inquired how he came to perpetrate such a 
crime, then, any one would be said to account for it, [to show 
why he did it,*] by saying that he was a man of ferocious and 
revengeful character ; or that he was known to bear malice 
against the deceased ; or to have an interest in liis death, &c. 
And these very circumstances might have been used (sup- 
posing the charge not proved) as an argument to cast suspicion 
on him. 

On the other hand, if his guilt were inferred from the testi- 
mony of some witnesses, or again, from his clothes having been 
bloody, or from his having about him some property of the de- 
ceased, these would be arguments of the other class, since they 
are such as could not have been employed to account for the 
fact, supposing it established. 

§ 7. The Arguments of this latter class may be subdi- 
vided into two kinds ; which may be called Arguments from 
' Sign,' and Arguments from ' Example ; ' [or ' Instance '] 
each of which may also be further subdivided. 

^. As far as any circumstance is what may be called a 
' Condition,'' — more or less necessary, — to the existence of 
a certain effect, phenomenon, event, result, law, &c. ; in other 
words, as far as it is a ' Condition ' of the truth of some asser- 

* It is to be observed that the Avord ' why ' has three different senses; 
viz. from wliat cauf^e ? by wliat i^roof? for what purpose ? 



158 DIFFERENT KINDS OF ARGUMENTS. [^Pavt V 

tion or supposition, — so far it (the ' condition ') may be infer- 
red [or ' concluded '] from the truth of that assertion or sup- . 
position, — from the existence of that effect, &c. 

If it be a ' Condition ' absolutely essential to something which 
we know or assume to be true, it may, of course, be inferred 
with complete certainty: and the nearer we approach to 
this case, the stronger will be the probability. 

Thus, in the instance just above, when a man is suspected 
of a murder, from being found near the spot, his clothes bloody, 
and property of the deceased about him ; the perpetration of 
tbe murder by him is just so far probable, as it is presumed 
to be a Condition of the existence of the ' Signs ; ' i. e. so far 
as it is presumed that otherwise his clothes would not have 
been stained, &c. [or that they would not have been stained 
unless he had committed the deed.] 

So also the wetness of the roads is a ' Sign ' that rain has 
fallen,' just so far as we suppose that otherwise the roads would 
?20^ have been wet; — in short, that the fall of rain was a 
condition of that wetness. 

To this head we may refer all mathematical reasonings. 
Every property, for instance, of a Triangle, may be regarded 
as a ' condition ' of the supposition that ' a Triangle,' is what 
is defined, A figure would not he a Triangle, unless its angles 
were equal to two right angles,' &c. 

It is to be observed, that although in many Arguments from 
* Sign' — as when we infer wetness of the roads from a fall 
of rain — we infer a Cause from an Effect, this is not inas- 
much as [or ' so far forth as '] it is a Cause, but inasmuch as 
it is a Condition. For we should no less infer from finding a 
certain spot wet, that it had been left uncovered ; though the 
mere absence of covering could not be properly called a Cause 
of its wetness. 

And in like manner, a man's having been alive on a certain 
day, might be inferred as a necessary ' Condition ' (though 
r-^rtainly not a ' Cause ') of his dying the next day. 



Lesson xvii.] arguments from sign. 159 

§ 8. ^Testimony' is one kind of 'Sign.' For it evidently 
has weight just so far as we suppose the truth of what is 
attested, to be a necessary ' Condition of the testimony ; that 
is, just so far as we suppose that the testimony would not have 
been given, unless the thing attested had been true. 

The different degrees of weight due to different Testimonies 
must, of course, depend on a great variety of circumstances : 
of which we must, on each occasion, judge in great measure 
from the particulars of the case then before us. 

There are two remarks, however, on this point, which are 
needful to be kept in mind : ist. we should remember the dif- 
ference between Testimony to ' matters-of-y«cif ' and to ' mat- 
ters-of-c»J9^?^^o?^.' When the question is about dt,fact, we look 
merely, or chiefly, to the honesty of the witness, and to his 
means of ohtaining information : when the question relates to 
doctrine [or opinion] of any kind, his ability to Judge must 
equally be taken into account. 

By a ' matter [or " question "] of fact,' is commonly under- 
stood something which might, conceivably, be submitted to the 
senses ; and about which it is supposed there could be no dis- 
agreement among persons who should be present, and to whose 
senses it should be submitted. 

By a ' matter-of-opinion,' again, is meant anything whereon 
an exercise o^ judgment would be called for on the part of 
persons having the same objects presented to their senses ; and 
who might, conceivably, disagree in their judgment. 

Suppose, ibr instance, a man is accused of a murder ; 
whether he did or did not strike the blow, or fire the shot, 
&c., would be a question o'i fact ; whether he did so wil- 
fully and. mcdiciously (wliich is necessary to constitute an 
act, murder) would bo a question of \Jjudgment,''2 or opinion. 

And observe, that the distinction does not at all turn on the 
greater or less degree of certainty attamable in the two cases 
respectively. For instance, whether King Richard the 3d 



I GO DIFFERENT KINDS OF ARGUMENTS. \_Part Y. 

did^ or did not, put to death his nephews in the Tower (which 
is a ' question o^fact,') is very doubtful, and a matter of dis- 
pute among historians : but what sort of an act it was, if he 
did commit it, is a ' matter of opinion,' but one on which no 
one would be likely to doubt. 

§ 9. In most cases this distinction is very obvious : but it 
sometimes happens that a person is supposed, — and supposes 
himself — to be attesting 21 fact, when in truth he is giving an 
opinion ; that is, either stating the inference he draws from 
the fact he has witnessed ; or again, professing to attest a fact 
which he has not really witnessed, but which he concludes to 
have taken place, from something he did witness. 

An instance of the former kind is, when some one who is in 
attendance on a sick person, bears witness that the patient 
was benefitted, or was disordered, hy taking such and such a 
medicine. He was an eye-witness, perhaps, of the medicine's 
being swallowed, and of the subsequent change for the better 
or for the worse; but that the medicine caused that change, 
(though he may be very right in believing that it did) is evi- 
dently l[i\s judgment. 

As an instance of the other kind, a man, suppose, will attest 
that he saw such one killed : though, perhaps, he did not see 
him dead ; but saw him receive a wound which he judged 
(perhaps very rightly) could not fail to occasion speedy death. 

For it is to be remembered that there may be, and often 
are, * questions-of-opinion ' relative to facts ; i. e., vje, judge 
from such and such circumstances, that so and so is, or is not, 
likely to occur ; or to exist. It is a fact that there is, or 
that there is not, a great lake in the interior of New-Hol- 
land ; but till that interior shall have been explored, every- 
one is left to form his opinions, and to judge according to 
probabilities. 

And hence, it should- also be remembered that men are apt 
to reason unconsciously ; and thus to suppose themselves bear- 



Lesson xvii.] matter of opinion. 161 

ing testimony (as has been said) to something their senses 
have witnessed, when in truth they are stating their own in- 
ferences therefrom. 

The process which usually takes place is this : their senses 
furnish them with one Premise, (the Minor) the other is sup- 
plied by their own mind ; and the Conclusion drawn from 
these two (as you may see in the above examples) is what 
they describe themselves as having witnessed. 

§ 10. lily. The other remark to be borne in mind, is, that 
when several independent witnesses [witnesses between whom 
there could have been no collusion'] attest the same thing, the 
weight of their testimony depends on this agreement, and not 
on the weight of each considered separately, or on the mere 
addition of these together. 

Thus, if a stranger, or one on whose veracity I have no re- 
liance, gives me intelligence of some remarkable transaction, 
or state of things, which he professes to have witnessed, de- 
scribing fully all the details, I may, perhaps, think it more 
likely than not that the whole story and all the particulars, are 
a fabrication. But if I receive the same account from another, 
and again from another person, (equally undeserving of cred- 
it) who could not have had any communication with the first, 
nor could have had access to any source of false information 
common to them all, I should at once believe them ; because 
the chances would be immeasurably great against several 
persons (however likely, each, to invent a story) having, in- 
dependently, invented the same story. 

And the force of evidence in such an argument depends 
mainly on the number mid minuteness of the particulars in the 
thing attested ; because the chances are- thus increased against 
an accidental coincidence. 

The same rnle applies not only to ' Testimony,' but to other 
' Signs' also. As when, (to refer to an example in the pre- 
ceding Lesson,) a person after swallowing a certain drug is 



.V 



162 DIFFERENT KINDS OF ARGUMENTS. [^PaH Y. 

attacked with such and such symptoms ; which may have been 
accidental ; if the same symptoms follow in another case, and 
another, &c., we are convinced at length that these cannot 
have been accidental coincidences, but that the drug caused 
the symptoms. 

§ 11. When we reason from a known case to another, or 
others, less known, under the same Class, this is called argu- 
ing from ' Example,' — by ' Induction,' — from ' Experience,* 
— by * Analogy,' — by * Parity-of-reasoning,' &c., all of which 
expressions, though not exactly synonymous, denote a process 
substantially the same. And the two cases, — the known and 
the unknown, — are said to be ' analogous," or ' parallel cases ; ' 
the common Class which they both fall under, being, the point 
of Resemblance or Analogy between the two. 

Thus, we show from the example of the French Revo- 
lution, and that of England in the time of Charles the 1st, 
that the extreme of Democracy is likely to lead to a military 
Monarchy. 

It is in this sense that we speak of ' making an Example 
of one who is punished for any faults ; so as to deter others 
by the expectation that a like fault in them will lead to their 
punishment. 

And it is thus that we learn to anticipate such and such 
weather, in certain situations, at certain seasons ; and in short, 
become acquainted with the general Laws of Mature. 

In all these cases we proceed, strictly speaking, by Analo- 
g}^ But this word is most usually employed in those argu- 
ments where the correspondence between the two cases is not 
so complete as to warrant a certainty in our conclusions. 
When the two cases do correspond completely, or nearly so, 
we usually employ the word Experience. 

Thus, a man w^ould be said to be convinced from ' Expe- 
rience ' that such and such a kind of diet, or of medicine, or 
of weather, is wholesome or unwholesome to himself; if he 



Lesson xvii.] argument by induction. 163 

had invariably observed like effects on a number of men, he 
might, perhaps, speak of Experience as having convinced him 
that this diet, &c. was wholesome or unwholesome for the 
whole human Species ; though in this, he would be more lia- 
ble to mistake : but if he conjectured the same with respect 
to some other Species of animal, every one would say that he 
was reasoning by ' Analogy.' 

§ 12. And here observe, that it is not strictly correct to 
speak of ' Knowing by Experience ' such and such a general 
truth ; or that so and so will take place under such and such 
circumstances. Not but that we may often have the most 
complete and rational assurance of general truths, or future 
events ; but, properly speaking, what we hnovj, ' hy experi- 
ence,' is, the past only ; and those individual events which 
we have actually experienced ; and any conviction concerning 
a general rule and concerning future occurrences, is what we 
judge fi'om Experience.* 

And this distinction is important to be remembered, be- 
cause, although (as we have said) there are numberless cases 
in which the conclusion thus drawn is not liable to mistake, 
many persons are apt — as was above remarked — to make 
mistakes as to what it is that they themselves, — or that oth- 
ers, — are, on each occasion, bearing witness to. 

A mere fact, or a number of individual facts, however 
strange they may seem to us, — that are attested by a person 
whose veracity we can fully rely on, we are justified in be- 
lieving, even though he be a man of no superior judgment. 
But if he states some general fact [or ' law '] as a thing ex- 
perienced by him, we should remember that this is his in- 
ference, from his experience. It may be a very correct 
one ; and it may be one in which no great ability is needed, 

* See the instance fonncrly cited from Hume of the argument that 
miracles arc contrary to experience,' &c. 



164 DIFFERENT KINDS OF ARGUMENTS. \_Part V. 

for forming a correct judgment ; but still the case is one in 
which his ahility, as well as veracity, is to be taken into 
account. 

For instance, a Farmer or a Gardener will tell you that 
he ' knows by experience ' that such and such a crop suc- 
ceeds best if sown in Autumn, and such a crop again, if sown 
in Spring. And in most instances they will be right : that 
is, their Experience will have led them to right conclusions. 
But what they have actually known hy experience, is, the 
success or the failure of certain individual crops. 

And it is remarkable, that for many ages all Farmers and 
Gardeners without exception were no less firmly convinced 
— and convmced of their knowing it by experience — that the 
crops would never turn out good unless the seed were soion 
during the increase of the Moon : sl belief which is now com- 
pletely exploded, except iu some remote and unenlightened 
districts. 

§ 13. In all cases, Arguments of the Class we are now 
speaking of, proceed on the supposition (which is the Major- 
premise) that ' what takes place, — or has happened — or 
which we are sure would happen — in a certain case, must 
happen, or take place, in a certain other similar [or analogous] 
case : or in all such cases.' 

The degrees of probability of this Major-premise will, of 
course, be infinitely various, according to the subject-matter. 
In the investigation of what are called ' physical-laws,' a sin- 
gle experiment, fairly and carefully made, is often allowed to 
be conclusive ; because we can often ascertain all the circum- 
stances connected with the experiment. Tlius, a Chemist, 
who should have ascertained by trial, that a specimen of Gold, 
or of some other metal before him, would combine with Mer- 
cury, would at once conchide tliis to be a property of that 
metal universally. 

In human transactions, on the contrary, it would be thought 



Lesson XVII.] INVENTED EXAMPLE. 165 

verj rash to draw a conclusion from a single occurrence ; or 
even from two or three. We make, in such cases, a wide 
' Induction ' (as it is called) of a number of individual instan- 
ces, [or ' examples '] before we venture to conclude universal- 
ly, — or even as a general rule — what is likely to be, for in- 
stance, the result of such and such a form of Government, — 
of the existence of Slavery, — of the diffusion of Education, — 
of Manufactories, &c. 

§ 14. We have said that we sometimes argue not only from 
what has actually happened in certain cases, but also from 
what we feel certain would happen in such and such a sup- 
posed case. Of this description are instructive ' Fahles ' [or 
* Parables,' ' Apologues,' ' Illustrations '] in which a general 
maxim [or ' principle 'J is inferred from a supposed case, 
analogous to that to which we mean to apply the maxim. 

Thus, the imprudence of a man who should hastily join the 
disciples of Jesus, without having calculated the sacrifices re- 
quired, and the fortitude expected of him, is illustrated by the 
supposed case of a man's beginning to build a house without 
computing the cost. 

So also Socrates argued against the practice of some of 
the Greek republics, who chose their Magistrates by lot, from 
the supposed case of mariners casting lots, loho should have 
the management of the vessel, instead of choosing the best 
Seaman. 

And Nathan's parable brought home to David a sense 
of the enormity of his own crime. Indeed, the ' golden 
rule ' of supposing yourself to change places with your neigh- 
bor, and reflecting what you would, then, think it right for 
him to do towards you, is merely an admonition to employ 
in one (very numerous) class of cases, such a mode of rea- 
soning. 

In every employment of what may be called (' fictitious ' 
?r] ' invented example,' [reasoning from a supposed case] the 



1 66 DIFFERENT KINDS OF ARGUMENTS. \^Part V 

argument will manifestly have no weight, unless the result 
that is supposed in the imaginary case, be such as one would 
fully anticipate. 

On the other hand, real instances have weight, even thougll 
they be such as one would not have expected. For instance, 
that all animals with horns on the head, should chew the cud, 
and should be destitute of upper cutting-teeth, is what no one 
would have originally conjectured ; but extensive observation 
has so fully established this as a universal rule, that a natu- 
ralist, on finding the skeleton of some unknown animal with 
horns on the skull, would at once pronounce it a ruminant, and 
would be certain of the absence of upper incisors. 

§ 15. When an Argument of the Class now before us, 
[from Example, Analogy, &c.] is opposed by denial of one 
of the Premises, it is usual, in ordinary discourse, to say, 
either, ^ the statement is not correct,^ which is denying the 
-M*7Zor-premise, — or ' this case does not apply,' [or is ^ not in 
point '] — or does not hold good in reference to the one be- 
fore us ; ' or ' the cases are not parallel : ' which amounts 
(as you will see on examination) to denying the Major-ipre- 
mise. 

Thus, if any one recommends to this patient a certain med- 
icine, as having been found serviceable in cases of Typhus, 
it might be either denied that it did prove serviceable in 
those cases, which would be a denial of the Minor) or again 
it might be denied that this patient's disorder is the same as 
those : which would be a denial of the il^'or-premise. 

And here observe, that two things may be very unlike in 
most respects, and yet quite alike — i. e. the Analogy may 
hold good — in the one point that is essential to the argument : 
or again, they may disagree in that one, though they are anal- 
ogous in many other points. 

And it is from inattention to this distinction, that just argu- 
ments from Analogy are often rejected, and fallacious ones 
admitted. 



Lesson xvii.] analogy. 167 

§ 16. For instance, in the Parables alluded to above, if a 
man should object that ' a lamb is a very different thing from 
a wife,' and ' a ship from a Republic,' the differences, every 
one would see, do not aifect the Analogy in question. 

On the other hand, there is an Analogy in many respects 
between all ' valuable-Articles ' that Man uses ; as corn, and 
iron or lead, and again (what are called the precious-metals) 
gold and silver. And as an increased supply of most of these 
articles, while it lowered their price, would not diminish 
their usefulness, and would thus prove a general benefit, some 
might infer that this would hold good in respect of gold and 
silver. 

If the earth should yield two bushels of corn, or two tons 
of iron or lead, for one that it now yields, these articles 
would be much cheaper ; while a bushel of corn would be as 
useful in feeding us, as now ; and so, with most other articles. 

But if the supply of gold or silver were thus doubled, the 
chief use of these being for coin, and the utility of coin de- 
pending on its value, the only important change would be, that 
a sovereign or a shilling would be twice as large as now ; 
and, therefore, twice as cumbrous. So that no advantage 
would result. 

It is manifest that in a train of Reasoning, it will often 
happen, that several of the different kinds of argument we 
have spoken of will be combined. Thus we may, perhaps, 
have to prove by several examples, the existence of a cer- 
tain ' Cause ; ' and from that Cause to infer a certain ' Effect ; ' 
and that effect again may be employed as a * Sign ' to infer 
a certain ' Condition,' &c. 



In this, and the preceding Lessons, several interesting sub- 
jects have been very slightly touched on, which may be found 



1 68 CONCLUSION. \^Part v. 

more fully treated of, and the views now taken more devel- 
oped, in treatises on those several subjects.* 

If you proceed, in following up this course of study, to pe- 
ruse such treatises, you will have been prepared, it is hoped, 
to find that perusal the easier and the more interesting, from 
what has been explained in these Lessons ; and you will be 
the better able to understand what is valuable in other 
Works on such subjects, and to detect anything that may be 
erroneous. 

* In the Elements of Ehetoric, Part I., the subjects of this last Lesson 
are more fully treated of. 



CONTENTS. 

[To be filled up by the Student.] 



Part I. ANALYTICAL INTRODUCTION. 



Lesson L, p. 13. 



Lesson II., p. 18. 



15 



170 CONTENTS. 

Lesson III., p. 23. 



Lesson IV., p. 29. 



Lesson V., p. 34. 



CONTENTS. 171 

Lesson VI., p. 46. 



Lesson VIL, p. 46. 



Lesson VIIL, p. 53. 



172 CONTENTS. 

Pabt II. COMPENDIUM. 



Lesson IX., p. 60. 



Lesson X., p. 68. 



Lesson XI., p, 80. 



CONTENTS. 173 

Lesson XII., p. 90. 



Lesson XIIL, p. 101. 



Lesson XIV., p. 109. 



15 



l74 CONTENTS. 

Part III. SUPPLEMENT. 



Lesson XV., p. 118. 



PART IV. FALLACIES. 



Lesson XVL, p. 133. 



CONTENTS. 175 

Part V. 
DIFFERENT KINDS OF ARGUMENTS. 



Lesson XVIL, p. 152. 



176 

INDEX. 

[Index to be made by the Student.] 



Lesson. § Page. 



i 



I 



INDEX. 177 

Lesson. § Page. 



178 INDEX. 

Lesson. § Page. 



I 



INDEX. 179 

Lesson. § Page. 



^^^ INDEX. 



Lesson. § Page. 



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